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BANCROFT 
LIBRARY 

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OF 

THE  UNIVERSITY 

OF  CALIFORNIA 


PROCEEDINGS 

OF  THE 

CALIFORNIA  ACADEMY  OF  SCIENCES. 

Third  Series. 
Math.-Phys.  Vol.  I,  No.  7. 


The  Apparent  Projection  of  Stars  upon  the 

bright  Limb  of  the  Moon  at  Occulta- 

tion,  and  Similar  Phenomena  at 

Total  Solar  Eclipses,  Transits 

of  Venus  and  Mercury, 

Etc.,  Etc. 


BY 


George  Davidson,  Ph.D.,  Sc.D. 


Issued  December  1,  1900. 


SAN  FRANCISCO: 

Published  by  the  Academy. 

1900. 


PUBLICATION    COMMITTEE. 

Charles  H.  Gilbert,  Chairman. 
William  E.  Ritter,  G.  P.  Rixford. 


\ 

EDITORS  OF  MATHEMATICAL-PHYSICAL  PUBLICATIONS. 

Irving  Stringham,  E.  P.  Lewis. 


PROCEEDINGS 

OF  THE 

CALIFORNIA  ACADEMY  OF  SCIENCES. 

Third  Series. 

Math.-Phys.  Vol.  I,  No.  7. 


The  Apparent  Projection  of  Stars  upon  the 
bright  Limb  of  the  Moon  at  Occupa- 
tion, and  Similar  Phenomena  at 
Total  Solar  Eclipses,  Transits 
of  Venus  and  Mercury, 
Etc.,  Etc. 


BY 


George  .Davidson,  Ph.D.,  Sc.D. 


Issued  December  1,  /goo. 


SAN  FRANCISCO: 

Published  by  the  Academy. 

1900. 


Digitized  by  the  Internet  Archive 

in  2008  with  funding  from 

Microsoft  Corporation 


http://www.archive.org/details/apparentprojectiOOdavirich 


|00   o  3^ 


THE  APPARENT  PROJECTION  OF  STARS  UPON 
THE    BRIGHT     LIMB    OF    THE    MOON    AT 
OCCULT ATION,  AND  SIMILAR  PHENOM- 
ENA AT  TOTAL  SOLAR  ECLIPSES, 
TRANSITS  OF  VENUS  AND 
MERCURY,  Etc.,  Etc. 

BY    GEORGE    DAVIDSON,   PH.D,   SC.D. 

Read  before  the  California  Academy  of  Sciences,  August  9,  1897. 


CONTENTS. 

Page. 

Introduction 64 

Geodetic  Observations  in  the  Sierra  Nevada 66 

Visibility  of  Jupiter's  Satellites 66 

Conditions  of  Steadiness  and  Unsteadiness  of  the  Atmosphere  67 
Observed   Occultations   of   Red   Stars  at  the  Bright  Limb  of 

the   Moon 73 

Other  Observed  Occultations  of  Stars  by  the  Moon,  and  of 

Stars  and  Satellites  by  Jupiter 75 

Similar  Phenomena  at  Total  Solar  Eclipses 81 

Similar  Phenomena  at  Transits  of  Venus  and  Mercury  Across 

the  Sun's  Disc 82 

Instructions  for  Observing  the  Transit  of  Venus 85 

Curious  Descriptions  of  the  Phenomena 87 

Errors  of  Observation 88 

Observations   of  Solar  Eclipses   under  Different  Atmospheric 

Conditions 89 

Graphic  Exhibition  of  Unsteadiness 92 

Official  Recognition  of  the  Factitious  Borders  of  the  Moon 

and  Sun 93 

Great  Elevations  for  Observation 94 

Precision  Observations  at  Low  Elevations 96 

Recapitulation  of  Phenomena  at  Observation 97 

Other  Important  Results  Affected 100 

Nearly  All  Measured  Diameters  Too  Larg  e 101 

[63]  November  15,  1900. 


173 


VflAfl  !M.i 

64  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  30  Ser. 

Introduction. 

This  paper  is  prompted  mainly  by  the  many  references 
made  by  astronomers  and  astronomical  publications  to 
"  Baily's  Beads"  in  cases  of  total  solar  eclipses;  to  the 
"black  drop"  and  "ligament"  in  transits  of  Mercury 
and  Venus  over  the  Sun's  disc;  to  the  projection  of  a  star 
upon  the  bright  body  of  the  Moon  at  immersion  or  emersion 
of  occultation;  to  stars  and  the  satellites  of  Jupiter  seen 
through  the  limb  or  body  of  that  planet  at  occultation ;  to 
planets  surrounded  by  an  atmosphere  of  great  depth;  and 
to  empirical  corrections  to  the  semidiameters  of  the  Sun 
and  Moon  at  meridian  transits. 

We  have  lately  examined  the  reports  of  the  observers  of 
the  transits  of  Venus  in  1874  and  1882 ;  of  the  transits  of 
Mercury  since  1878,  and  the  reports  of  the  total  solar 
eclipses  since  i860;  and  we  are  amazed  at  the  crude  and 
apparently  indigested  explanations  given  for  certain  appear- 
ances attending  the  phenomena.  There  would  seem  to 
have  been  a  desire  to  seek  explanations  in  some  obscure 
cause  or  causes — such  as  the  poor  character  of  the  objective 
used,  the  lack  of  sharpness  in  the  limbs  of  the  planets 
(owing  to  their  possessing  an  atmosphere),  diffraction, 
telescopic  and  occular  irradiation,  astigmatism,  "sympathetic 
attraction,"  etc. 

These  explanations  are  very  unsatisfactory,  and  the 
experienced  observer,  who  has  observed  occultations  of 
stars  by  the  Moon  or  by  Jupiter,  meridian  transits  of  the 
Moon,  transits  of  Mercury  and  Venus  across  the  Sun's 
disc,  and  total  solar  eclipses  in  a  serene  atmosphere,  knows 
that  the  outlines  of  the  planets,  the  Moon,  and  the  Sun  are 
remarkably  sharp  and  steady,  even  under  high  magnifying 
power;  that  the  observations  made  under  such  conditions 
are  satisfactory;  and  that  there  are  no  extraordinary  phe- 
nomena present. 

In  such  an  atmosphere  the  spurious  disc  of  a  star,  large 
or  small,  moves  along  the  horizontal  thread  of  the  Meridian 
Circle,  or  the  Zenith  Telescope,  so  steadily  that  the  error 


M.-P.-Vol.  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.  65 

of  observation  should  not  exceed  one-tenth  of  a  second  of 
arc.  And  the  double-star  observer  certainly  expects  his 
measures  of  distance  to  differ  little  from  that  amount.  In 
the  telescope  the  diffraction  rings  of  the  stars  are  beauti- 
fully delicate.  On  a  quiet  night  the  stars  appear,  to  the 
normal  eye,  fixed  on  the  sky  like  minute  dots  of  light,  with- 
out a  sign  of  twinkling  or  irradiation,  and  the  intensity  of 
the  light  of  each  star,  large  or  small,  is  continuous. 

The  observer  knows  that  in  an  atmosphere  which  is 
remarkably  unsteady,  when  every  star  to  the  naked  eye  is 
dancing  madly,  the  smallest  stars  have  disappeared,  the 
smaller  ones  appear  and  disappear  spasmodically,  and  the 
larger  ones  near  the  horizon  rapidly  change  color,  and 
even  the  planets  have  much  irradiation  and  are  blinking; 
the  star  in  the  instrument  has  lost  its  diffraction  rings,  the 
spurious  disc  is  broken  up,  and  the  confused  mass  jumps 
wildly  across  the  micrometer  thread  and  frequently  expands 
into  a  nebulous  film  many  seconds  in  diameter.  We  have 
measured  such  an  apparition  of  Polaris  forty-seven  seconds 
in  diameter. 

"  Burnham  has  remarked  that  an  object-glass  of  six 
inches  will  one  night  show  the  companion  of  Sirius  per- 
fectly; on  the  next  night,  just  as  good  in  every  respect, 
so  far  as  one  can  tell  with  the  unaided  eye,  the  largest 
telescope  in  the  world  will  show  no  more  trace  of  the  small 
star  than  if  it  had  been  blotted  out  of  existence."  (Webb's 
"  Celestial  Objects.") 

With  a  serene  atmosphere  the  transit  observer  is  certain 
of  his  times.  With  a  disturbed  atmosphere  he  can  make 
only  an  unsatisfactory  estimate  by  eye  and  ear,  and  a  still 
less  reliable  one  by  the  chronograph. 

In  the  course  of  fifty-four  years'  experience  as  an 
observer,  largely  in  the  field,  we  have  encountered  a  range 
of  physical  conditions  that  falls  to  the  lot  of  very  few.  We 
have  made  astronomical  and  geodetic  observations  in  all 
climates,  at  all  seasons,  from  the  low  ocean  coast  to  eleva- 
tions reaching  12,566  feet,  and  with  instruments  of  precision 
of  various  character.     Our  latest  astronomical  observations 


66  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

were  made  in  perhaps  the  worst  locality  possible.  The 
peninsula  of  San  Francisco  near  the  Golden  Gate  is  unique 
for  general  unsteadiness  of  the  atmosphere,  yet  marked  on 
rare  occasions  by  some  supreme  exhibitions  of  quietness. 

Geodetic  Observations  in  the  Sierra  Nevada. 

In  the  high  Sierras  of  eastern  California,  from  7,250  to 
10,430  feet  elevation,  after  a  great  southeast  storm  with 
clearing  weather  in  the  night,  a  strong  wind  from  the  north- 
west, and  a  wonderfully  pellucid  sky  and  steady  atmosphere 
to  windward  that  gave  astonishing  clearness,  sharpness, 
steadiness  and  apparent  nearness  to  all  objects,  we  have,  at 
the  greater  elevation,  seen  star-like  heliotrope  images  with 
the  naked  eye,  at  stations  120,  130,  140  and  160  miles 
distant  to  the  west  and  northwest,  whence  the  cold,  keen 
wind  was  blowing.  At  this  station,  with  the  whole  range 
covered  with  snow,  the  mountain  face  was  precipitous  for 
1,356  feet  to  the  north.  To  the  southeastward  and  east- 
ward, over  the  very  deep  valley  of  the  Mokelumne  River, 
directly  under  us,  subject  to  the  Sun's  early  warmth,  the 
atmosphere  became  excessively  disturbed  and  the  heliotrope 
images  in  that  direction  were  not  visible  to  the  eye  at  dis- 
tances of  forty  miles.  In  the  telescope  the  former  images 
were  steady,  round,  and  so  minute  that  the  micrometer 
thread  nearly  covered  them;  the  latter  images  were  very 
diffuse,  irregular  and  unsteady,  and  ranged  from  twenty 
seconds  to  thirty  seconds  in  diameter.  In  the  first  case  the 
pointing  was  quickly  and  satisfactorily  made;  in  the  second 
the  pointings  were  unsatisfactory,  even  with  half  a  dozen 
occular  pointings  as  checks. 

Visibility  of  Jupiter's  Satellites. 

In  astronomical  work  we  have  observed  the  Sun,  Moon, 
planets  and  stars  when  the  Sun  was  serenely  steady;  and 
at  night  not  a  star  twinkled  to  the  naked  eye,  and  no  irra- 
diation was  visible  to  Jupiter.  Half  a  dozen  times  in  our 
experience  we  have  been  able  to  distinguish  with  the  naked 


+ 


(/l^lv/wiH 


**^&#>*~**v 


M.-P.— Vol.  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.  6*] 

eye1  two  of  Jupiter's  satellites,  when  close  together,  as  one; 
and  at  one  mountain  station  (3,200  feet  elevation)  all  the 
members  of  our  party  witnessed  a  similar  phenomenon. 
Very  curiously,  that  evening  was  slightly  hazy,  and  very 
faint  stars  were  not  visible ;  but  the  atmosphere  was  remark- 
ably steady.  Under  atmospheric  condition  of  supreme 
quietness  we  have  placed  eleven  stars  in  the  Pleiades. 
^j  The  visibility  of  Jupiter's  satellites  by  the  naked  eye  has 
generally  been  received  with  much  doubt.  Humboldt,  in 
his  Cosmos,  has  related  a  well  authenticated  case,  but  we 
can  come  to  our  own  observers  for  confirmation.  At  the 
time  of  the  total  solar  eclipse  of  August,  1878,  one  of  the 
United  States  Naval  Observatory  observers  in  Colorado  saw 
with  the  naked  eye  three  satellites  of  Jupiter  separately  — 
two  very  distinctly  and  one  less  so.  The  atmosphere  was 
supremely  serene,  and  the  station  (Idaho  Springs)  7,548 
feet  above  the  sea.  Two  other  persons,  not  observers,  also 
witnessed  the  phenomenon.  In  1874  tne  Professor  and  his 
colleagues  had  doubted  my  seeing  even  two  satellites  close 
together  as  one. 

Conditions  of  Steadiness  and  Unsteadiness  of 
the  Atmosphere. 

Under  similar  atmospheric  conditions  the  limbs  of  the 
Sun,  Moon  and  planets  are  sharply  defined  and  remarkably 
steady;  the  Sun-spots  are  beautifully  distinct  and  their 
changes  of  form  readily  followed;  the  irregularities  of  the 
outline  of  the  Moon  are  unmistakable;  the  spurious  discs  of 
the  stars  are  encircled  by  delicate  diffraction  rings,  and 
the  overlapping  spurious  discs  of  very  close  double  stars 
present  new  forms.  Under  conditions  of  supreme  steadi- 
ness of  the  atmosphere,  we  believe  that  an  observer  with 
keen  eyesight  should  see,  with  unassisted  vision,  the  larger 
satellites  of  Jupiter,  when  favorably  located,  and  from  ten 
to  twelve  stars  in  the  Pleiades.  Either  is  a  severe  and 
unique  test  of  steadiness  and  eyesight.  In  these  periods  of 
great  steadiness  the  observer  aches  for  finer  micrometers, 
higher  power,  and  more  stable  instruments. 

1  Except  with  spectacles  for  short-sightedness. 


68 


CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 


0    h 


When  the  steadiness  of  the  atmosphere  begins  to  break, 
the  images  of  the  Sun,  Moon  and  planets  exhibit  occasional 
tremors  or  shiverings;  and  even  when  this  vibratory  move- 
ment has  become  nearly  continuous,  but  not  rapid,  the 
actual  and  apparently  more  condensed  outline  of  the  image 
can  be  selected  for  measures  of  precision  in  moments  of 
quietude.  As  the  unsteadiness  of  the  atmosphere  increases, 
the  vibration  of  the  limbs  increases  in  rapidity  and  ampli- 
tude until  there  is  finally  created  a  blurred  outline  of  Sun, 
Moon  or  planet,  which  necessarily  presents  an  increased 
diameter  of  the  object.  The  stars  are  similarly  affected; 
with  the  first  signs  of  unsteadiness  in  the  atmosphere  the 
diffraction  rings  are  broken,  and  disappear  as  the  unsteadi- 
ness increases;  the  spurious  disc  is  broken  into  pieces;  its 
march  is  peculiar,  in  presenting  one  fragment  after  another 
with  more  or  less  frequency,  but  may  continue  with  a  waltz- 
ing movement  until  the  unsteadiness  has  increased  and  the 
spurious  disc  is  without  form,  dilated,  jumping  wildly  in 
every  direction,  and  a  wretched  object  for  observation. 

Similar  conditions  are  exhibited  by  geodetic  signals  of 
all  classes.  In  a  serene  atmosphere  poles  are  seen  very 
steady  as  fine,  sharp  images,  sometimes  finer  than  the 
micrometer  threads.  When  this  atmosphere  is  disturbed, 
tremors  or  shiverings  carry  the  images  to  right  or  left  one 
or  more  diameters,  and  the  observer  selects  moments  of 
quietude  for  first-class  observations;  finally,  as  the  unsteadi- 
ness of  the  atmosphere  increases,  the  images  become  large, 
confused,  blurred  and  faint,  and  observations  are  difficult  to 
make  and  unsatisfactory.  In  the  quiet  atmosphere,  white 
poles  five  feet  long  and  four  and  six-tenths  inches  in  diameter, 
projected  upon  a  dark  background,  have  been  seen  with  the 
naked  eye  at  distances  of  four  and  one-half  miles  across 
water.  In  times  of  great  unsteadiness  and  equally  clear 
atmosphere  they  are  difficult  to  see  in  the  telescope. 

Heliotrope  images  behave  precisely  as  those  of  the  stars. 
On  a  certain  line  of  the  main  triangulation  of  the  Pacific 
Coast,  where  plains,  several  mountain  ridges  and  inter- 
vening valleys  were  crossed  by  the  line  of  sight,  and  where 


M.-P.— Vol.  I.]     DA  VIDSON— APPARENT  PROJECTION,  ETC.  69 

the  cold  ocean  air  sweeping  through  the  Karquinez  Strait 
added  ten-fold  confusion,  the  heliotrope  image  from  Mt. 
Diablo,  distant  forty-five  miles,  was  seen  in  the  telescope 
like  the  waving  flame  from  the  stack  of  a  smelting  furnace. 
Sometimes  the  image  exceeded  sixty  seconds  in  irregular 
diameter,  and  its  horizontal  direction  was  very  abnormal. 
This  condition  lasted  for  many  days.  When  the  air  became 
of  more  uniform  temperature  the  image  was  small,  star- 
like, and  steady,  and  its  direction  normal. 

In  the  remarkably  quiet  atmosphere  of  the  mountains, 
before  sunset,  with  a  pure  sky  for  a  background,  we  once 
saw,  with  the  two  and  one-eighth  inches  objective  of  the 
theodolite,  the  observer  leave  his  station,  which  was  thirty- 
three  miles  distant  from  Mt.  Tamalpais.  With  a  salmon- 
colored  sky  in  the  west,  and  the  atmosphere  remarkably  clear 
and  steady,  Superintendent  Bache  observed  upon  the  signal- 
pole  of  Mt.  Wachusett,  distant  sixty-one  miles.  The  image 
was  nearly  as  dark  and  sharp  as  the  cross-threads. 

In  winter,  at  great  elevation,  we  once  saw,  with  a  three- 
inch  objective,  just  after  sunrise,  with  a  serene  atmosphere, 
the  heliotroper  projected  against  a  snow  background  at  a 
distance  of  fifty-one  miles.  From  Mt.  Diablo,  3,849  feet 
elevation,  with  the  same  size  objective,  just  before  sunrise, 
in  a  perfectly  quiet  atmosphere,  when  the  crest-line  of  the 
Sierra  Nevada  was  projected  like  a  dark-blue  saw  against 
the  warm  eastern  sky,  and  apparently  only  thirty  or  forty 
miles  distant,  we  saw  upon  several  mornings  the  observing 
hut  on  the  pinnacle  of  Mt.  Conness.  The  hut  was  six  feet 
wide  by  seven  and  a  half  feet  high,  and  the  distance  one 
hundred  and  forty-three  miles ;  the  width  therefore  sub- 
tended i".6^.  After  the  hut  had  been  cut  down  to  about 
four  feet  we  still  made  it  out  upon  an  extraordinarily  clear 
and  steady  morning.  On  account  of  the  distance  and  great 
.  height  of    Mt.  Conness  (12,566  feet)  the  Sun  rose  to  the 

TJi/uXXausixj  heliotroper  about  eight  minutes  earlier  than  to  Mt.  Diablo. 
The  sharpness  and  steadiness  of  Mt.  Conness  were  supreme, 
and  the  image  of  the  heliotrope  was  like  a  minute  star;  but 
so  soon  as  the  Sun's  rays  struck  the  eastern  flank  of  Mt. 


"*  /fltA^ 


J-*'*'** 


feWfc  .fttUy  /     del  Muerte 

We  have 


70  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

Diablo  the  atmosphere  around  the  observing  station  became 
so  unsteady  that  observations  were  made  with  difficulty  and 
little  satisfaction. 

We  had  a  similar  experience  at  the  transit  of  Venus, 
Station  Cerro  Roblero,  in  New  Mexico,  in  1882.  Before 
sunrise  the  atmosphere  was  so  serene  that  we  could  see, 
with  the  five-inch  equatorial,  the  small  branches  of  the  scant 
scrub  growth  on  the  dark,  sharp,  blue  crest-line  of  the 
Organ  Mountains,  twenty  miles  distant.  Immediately  after 
sunrise  the  suddenly  heated  air,  rising  up  the  steep  slope  of 
the  Cerro  Roblero,  just  in  front  of  the  observatory,  caused 
great  waves  of  disturbed  air  to  obliterate  the  branches  of 
the  brush  and  to  exhibit  the  border  of  the  Sun  as  a  remark- 
ably confused  outline.  The  direction  of  these  waves  was 
very  marked.  At  the  time  of  the  first  contact  of  the  images 
of  Venus  and  the  Sun  the  observations  were  made  with 
difficulty  and  doubt,  and  micrometer  measures  were  almost 
impracticable.  The  station  was  about  5,676  feet  above  the 
sea,  and  1,655  ^eet  above  the  Rio  Grande  and  the  Jornado 


We  have  been  thus  prolix  in  order  to  indicate  that  the 
principal  disturbance  exhibited  in  the  telescope,  as  well  as 
to  the  unassisted  eye,  is  in  the  immediate  vicinity  of  the 
observing  station.  At  trigonometrical  stations,  in  disturbed 
conditions  of  the  air,  the  confused  and  unsteady  image  of  a 
heliotrope  will  exhibit  a  movement  of  5"  to  15"  of  arc.  The 
observer  could  not  see  such  movement  if  it  took  place 
rapidly  at  the  distant  station.  If  the  heliotrope  image  at 
Mt.  Connesswere  moved  bodily  sideways  forty-four  inches, 
the  observer  at  Mt.  Diablo  would  see  it  change  only  one 
second  in  amplitude,  supposing  the  movement  were  slow 
and  therefore  capable  of  cognizance,  instead  of  being  very 
rapid  and  not  then  capable  of  detection.  This  exhibition  of 
the  locally  disturbed  atmosphere  at  the  observing  station  can 
be  readily  produced  artificially. 

At  Round  Top  station,  in  the  Sierra  Nevada,  10,435  feet 
elevation,  we  counted  forty-seven  forest  fires  that  arose  on 
the  flanks  of   the  forested  mountains  over  which  we  were 


M.-P.— Vol.  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.  7 1 

observing.  The  smoke  gradually  filled  the  Sacramento 
Valley  to  a  height  of  10,000  feet,  and  obscured  the  outline 
of  the  Coast  Range  Mountains;  but  we  observed  the  helio- 
tropes through  this  irregularly  heated  atmosphere  with  little 
difficulty,  and  at  the  close  of  the  operations  the  probable 
error  of  a  direction  was  only  seven  hundredths  of  a  second 
of  arc. 

Besides  the  disturbance  of  the  outer  atmosphere  near  the 
observer,  there  is  another  source  of  disturbance  in  the  air 
within  the  tubes  of  the  great  telescopes,  especially  in  sun- 
light observations  or  at  the  sudden  change  of  temperature 
at  sunset.  This  is  visibly  exhibited  in  the  blurred,  unsteady 
and  confused  outline  of  the  Sun  and  the  Sun-spots  projected 
upon  the  ground-glass  plate  of  the  horizontal  heliograph 
tubeless  telescope  of  forty-feet  focus.  In  the  transit  of 
Venus  of  1882  the  image  of  the  Sun  at  Cerro  Roblero  was 
projected  through  a  forty-feet  tin  tube  of  large  diameter, 
and  was  much  blurred;  but  this  was  largely  corrected  when 
the  tube  was  covered  with  a  wooden  roof  not  in  contact. 

Professor  A.  E.  Douglass,  of  the  Lowell  Observatory, 
has  shown  that  the  waves  of  the  disturbed  atmosphere  out- 
side and  inside  of  the  large  telescope  tubes  are  distinctly 
visible  to  the  naked  eye  when  it  is  placed  in  the  focus  of 
the  objective,  as  in  the  Foucault  test.  And  even  more  than 
one  series  of  such  waves  of  disturbance  at  different  dis- 
tances and  moving  in  different  directions  is  not  infrequent. 

It  is  well  known  that  to  obtain  the  best  results  with  the 
great  telescopes  it  is  imperative  that  the  air  inside  the  dome 
and  inside  the  telescope  tube  shall  have  the  temperature  of 
the  outside  atmosphere. 

At  Arequipa,  Peru,  the  Harvard  Observatory  was  situated 
close  to  the  valley  of  a  mountain  stream  or  arroyo,  down 
which,  on  clear  nights,  a  swift  stream  of  cold  air  descends. 
Whenever  this  cold  stream  overflowed  the  banks  and  envel- 
oped the  observatory,  and  rose  to  the  height  of  the  objective, 
the  seeing  was  immediately  ruined  for  the  rest  of  the  night. 
In  such  circumstances,  if  the  eye-piece  of  the  telescope  was 
removed  and  the  eye  placed  in  the  focus,  fine  parallel,  dark 


72  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3d  Ser. 

lines   could  be  seen  moving  swiftly  lengthwise  across  the 
illuminated  lens  in  the  direction  of  the  wind.1 

At  San  Francisco,  in  the  strong  "wind  gap"  of  the 
Golden  Gate,  it  sometimes  happens  at  sunset,  after  a  calm, 
moderate  day,  that  star  images  are  disc-like  and  steady;  in 
a  few  minutes  the  westerly  wind  rises  and  brings  in  the  fog- 
chilled  air  from  the  ocean,  with  flying  patches  of  fog  over- 
head, and  the  star  images  at  once  become  diffused  and 
nebulous,  with  an  unsteadiness  reaching  an  amplitude  of 
5" to  10"  of  arc. 

Large  volumes  of  air,  each  of  different  but  uniform  tem- 
perature, projected  across  a  line  of  sight  at  a  great  distance 
from  the  observer,  do  not  necessarily  produce  abnormal 
images  of  a  star  or  heliotrope;  they  seem  to  act  as  prisms, 
and  deflect  the  line  of  light  so  as  to  exhibit  abnormal  hori- 
zontal or  vertical  refraction  without  any  marked  unsteadi- 
ness. Along  the  face  of  a  great  mountain  wall  we  have 
measured  a  slow  change  of  azimuth  of  a  signal  amounting 
to  65"  of  arc,  due  to  the  gradual  rising  of  the  morning  tem- 
Cavvw  I  peratureof  the  air  immediately  adjacent  to  the  eastern  rocky 

Cr  ^  face  of  Mt.  Constitution. 

There  are  so  many  conditions  conspiring  to  a  disturbed 
atmosphere  that  it  necessarily  acts  in  various  ways  difficult 
to  predict.  Where  there  are  regular,  irregular  or  confused 
atmospheric  waves  moving  at  different  distances  from  the 
objective,  and  in  different  directions,  they  necessarily  give 
different  images  of  the  star  at  different  foci,  and  at  each 
change  they  bodily  shift  the  image  near  the  focus,  and  also 
change  its  form.  Professor  Douglass'  observations  are  very 
instructive  in  this  matter. 

When  volumes  of  unusually  heated  air  pass  over  the 
objective  they  may  act  as  a  species  of  air  lens  which  sud- 
denly and  irregularly  spreads  out  the  image  of  the  star  at 
the  focus;  but  no  change  of  focus  will  bring  the  image  to 
condensation.  This  we  first  experienced  at  Point  Concep- 
cion  in  1850,  where  the  perceptibly  hot  volumes  of  air  from 

1  Douglass,  "  The  American  Meteorological  Journal,"  March,  1895,  p.  395. 

^^^^(7^^^*^.  A^+^£r/&~»  Ay*4. 


M.-P.— Vol.  I.]     DA  VIDSON— APPARENT  PROJECTION,  ETC.  73 

the  higher  gulches  were  driven  over  the  observatory  by  an 
incoming  cold  north  wind  from  the  Sierra  Santa  Inez. 

It  is  sometimes  reported  that  stars  become  very  unsteady 
in  a  strong  wind;  yet  we  have  determined  micrometer 
values  by  observations  upon  a  close  circumpolar  star  during 
a  fierce  "  norther."  In  geodetic  observations  between  Mt. 
Diablo  and  Mt.  Conness,  on  a  line  of  143  miles  across  the 
Sacramento  Valley,  we  witnessed  a  strong  norther  blowing 
down  the  valley  and  carrying  vast  quantities  of  dust  across 
the  line  of  sight;  but  the  wind  did  not  reach  the  observing 
station  on  the  first  day,  when  the  heliotrope  image  was 
fairly  good,  but  was  moved  bodily  by  horizontal  refraction 
two  or  more  seconds  of  arc  from  the  normal  direction. 

Observed  Occultations  of  Red  Stars  at  the 
Bright  Limb  of  the  Moon. 

Referring  now  more  particularly  to  the  details  of  some 
astronomical  observations,  we  give  a  few  instances  from  our 
experience  and  that  of  others. 

On  September  18,  1848,  about  seven  and  one-half  hours 
in  the  morning,  we  observed  the  occultation  of  a  Tauri  by 
the  bright  limb  of  the  Moon,  using  a  telescope  of  probably 
two  and  one-half  inches  aperture  and  moderate  power. 
The  red  star  touched  the  bright  limb,  and  we  noted  the 
time  mentally,  because  it  did  not  instantly  disappear.  We 
continued  the  watch  until  the  star  was  unmistakably  within 
the  apparent  limb,  when  it  disappeared  instantly,  about  two 
and  a  half  seconds  after  the  first  apparent  contact.  We  at 
once  submitted  the  case  to  our  chief,  R.  H.  Fauntleroy, 
who  said  the  disappearance  was  the  true  time  of  the  occul- 
tation, but  he  gave  no  explanation  of  the  phenomenon.  We 
then  submitted  the  observation  to  the  Superintendent  of  the 
United  States  Coast  Survey,  Professor  A.  D.  Bache,  who 
wrote  to  the  Royal  Astronomer  (Airy)  on  the  subject. 
The  reply  was  that  he  personally  had  never  observed  the 
phenomenon,  but  there  were  similar  cases  on  record.  He 
gave  no  explanation. 

no  />  v^      *  Hj*Ja  ^^/Miu,  i^U^U^  y^<^ys*^n* 


74  CALIFORNIA   ACADEMY  OF  SCIENCES.      [Proc.  3d  Ser. 

In  the  trigonometrical  survey  of  Admiralty  Inlet  and 
Puget  Sound,  during  the  approach  of  a  southeast  storm 
which  finally  brought  up  dense  clouds,  a  heavy  squall  and 
rain,  we  observed  a  Scorpii  (April  22,  1856,)  with  a  three- 
inch  Fraunhofer  telescope  and  astronomical  eye-piece,  power 
about  70.  The  disappearance  of  the  star  was  behind  the 
bright  limb,  and  the  record  states  that  "  the  time  denotes 
the  instant  of  the  disappearance  of  the  star  after  it.  had  been 
projected  upon  the  body  of  the  Moon  for  about  two  and  one- 
half  seconds,  certainly  not  less.  The  ruddy  color  of  the  star 
showed  distinctly  upon  the  body  of  the  Moon,  and  the 
instant  of  disappearance  was  as  accurately  noted  as  if  it 
had  disappeared  behind  the  dark  limb.  Having  once  before 
observed  the  same  phenomenon,  we  were  fully  prepared 
for  it." 

In  November,  1886,  we  presented  a  paper  to  the  Cali- 
fornia Academy  of  Sciences  upon  the  occultation  of  a  Tauri 
on  the  twelfth  of  November.  Three  instruments  were  used 
at  the  disappearance:  two  three-inch  Fraunhofers,  power 
100,  and  a  two-inch,  power  55.  The  atmosphere  was  clear 
and  moderately  steady,  the  stars  showed  signs  of  unsteadi- 
ness, and  the  Moon's  border  appeared  reasonably  sharp. 
The  telescopes  were  not  large  enough  for  such  observa- 
tions, but  an  intervening  house  prevented  the  use  of  the  six 
and  four-tenths  inches  Equatorial. 

The  star  was  visible  to  the  unassisted  eye  to  within  four 
minutes  of  contact.  When  it  was  a  few  seconds  from  the 
Moon's  bright  limb  the  star  became  invisible  in  the  two-inch 
telescope.  In  the  three-inch  Fraunhofers  the  star  did  not 
disappear  when  it  touched  the  apparent  limb  of  the  Moon, 
but  continued  to  move  upon  the  disc  until  it  was  fully  one 
and  one-half  times  the  diameter  of  its  spurious  disc  on  the 
Moon,  when  it  disappeared  with  the  instantaneity  of  such 
phenomena.  The  star  grew  somewhat  difficult  to  see  after 
it  entered  upon  the  factitious  limb,  but  its  reddish  hue  left 
no  doubt  in  the  minds  of  the  two  observers,  who  differed 
0.07  second  in  the  time  of  its  disappearance.  They  esti- 
mated that  it  was  three  seconds  of  time  on  the  limb.     At 


&4h# 


/flu  <*c£^£>  V^< 


M.-P.— Vol.  I.]     DA  VIDSON— APPARENT  PROJECTION,  ETC.  75 

emersion  from  behind  the  narrow,  dark  edge  of  the  Moon 
(which  was  one  day  past  the  full)  the  6.4-inch  Equatorial 
noted  the  reappearance  0.17  second  earlier  than  the  two 
three-inch  telescopes. 

At  the  Chabot  Observatory,  thirty-six  seconds  of  time 
east  of  the  Davidson  Observatory,  the  observer  used  the 
Clark  eight-inch  Equatorial  for  the  same  occultation.  The 
atmospheric  conditions  were  nearly  the  same  as  mentioned. 
The  star  advanced  upon  the  apparent  limb  of  the  Moon, 
but  not  so  far  as  above  mentioned,  and  some  of  the  apparent 
rays  of  the  star  projected  outside  the  Moon's  border. 

On  March  29,  1887,  we  observed  the  immersion  of 
a  Tauri  at  the  dark  limb,  and  the  emersion  at  the  bright 
limb;  the  former  by  daylight,  and  the  ash-gray  limb  not 
visible.  The  disappearance  was  instantaneous.  At  reap- 
pearance the  Moon's  limb  was  blurred  and  very  unsteady, 
and  the  star  reappeared  upon  this  blurred  bright  image 
inside  of  the  outermost  limit,  which  was  very  fuzzy  and 
decreasing  in  brightness  outward.  The  star  was  not  so 
bright  as  anticipated,  but  its  almost  sparkling  red  color  left 
no  doubt  whatever  in  our  mind  as  to  the  nearest  tenth  of  a 
second  of  the  epoch.  The  star  left  the  limb  in  two  and  one- 
half  or  three  seconds,  when  it  appeared  much  brighter.  At 
emersion  a  power  of  250  was  employed-  ♦ 

We  do  not  mention  the  hundred  and  more  occultations 
which  we  have  observed  when  the  above  phenomenon  was 
not  present,  or  when  the  smallness  and  whiteness  of  the  star 
may  have  prevented  its  detection. 

Other    Observed    Occultations    of    the    Stars    by 

the    Moon,    and    of    Stars    and    Satellites 

by    Jupiter. 

In  1890,  the  Astronomer  Royal  called  the  attention  of  the 
Royal  Astronomical  Society  to  the  occultations  of  f  Tauri 
(3.0  magn.)  that  presented  matter  of  ''interest"  to 
observers  and  astronomers.  On  September  16,  1889,  Mr. 
Turner,  of  the  Greenwich  Observatory,  observed  the  occul- 
tation of  the  same  star  by  the  bright  limb  of  the  Moon  with 


76  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

the  Lassell  Reflector  of  thirty-four  inches,  and  Mr.  Lewis 
with  a  refractor  of  three  and  three-fourths  inches.  Mr. 
Turner  noted:  "No  projection;  disappeared  instantaneously 
at  bright  limb."  Mr.  Lewis  noted  that  "  the  star  touched  the 
limb  of  the  Moon  five  seconds  before  the  observation,  and 
was  slightly  inside  the  limb."  It  appeared  "  as  a  brilliant 
spot  in  the  Moon,  and  disappeared  suddenly  at  the  time 
given  above."  In  the  same  number  of  the  "  Observatory  " 
where  this  report  is  made  Mr.  Ranyard  says  that  "  in  the 
case  of  Jupiter  there  are  instances  *  *  *  where  one  or 
two  stars  have  apparently  been  seen  through  the  limb  of  the 
planet.  There  are  such  a  number  of  these  observations  that 
we  cannot  doubt  the  planets  have  not  a  sharp  limb;  they 
seem  to  be  surrounded  by  an  atmosphere  of  great  depth,  or 
rather  a  gaseous  envelope,  in  which  clouds  or  dusty  matter 
float  in  irregular  masses."  This  is  an  extraordinary  state- 
ment, and,  in  our  judgment,  based  upon  a  misconception  of 
the  cause  of  these  phenomena. 

The  outline  of  any  cloud  system  at  such  enormous  dis- 
tances from  the  Earth  as  Mars,  Jupiter  and  Saturn  would 
subtend  so  minute  an  angle  that  the  outline  of  the  planet 
would  necessarily  appear  sharp,  even  if  the  assumed  cloud 
were  irregularly  distributed.  The  Sun's  outline  appears 
remarkably  sharp  when  our  atmosphere  is  steady,  and  yet 
we  know  that  extraordinary  disturbances  of  the  solar 
surface,  far  beyond  our  experience,  are  constantly  taking 
place. 

On  May  10,  1895,  Mr.  John  Tebbutt  observed  the  occul- 
tation  of  Antares  at  Windsor,  New  South  Wales.  The 
steadiness  and  definition  of  objects  were  reported  very  sat- 
isfactory. The  instrument  was  an  eight-inch  objective, 
with  a  magn.  power  of  74,  and  "Antares,  quite  brilliant  to 
the  last  moment,  was  closely  watched  till  it  came  into  con- 
tact with  the  bright  limb;  but  then,  instead  of  instantly 
disappearing,  it  seemed  to  cut  its  way  into  the  disc  during 
two  or  three  seconds,  and  vanished  instantaneously.  The 
reappearance  of  Antares  (62  1-3  minutes)  later  at  the  dark 
limb  was  remarkably  instantaneous."     It  should  be  noted 


M.-P.-Voi..  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.  77 

however,  that  the  observer  was  not  looking  at  the  spot 
where  the  star  reappeared,  and  thereby  lost  the  earlier 
reappearance  of  the  well-known  companion;  and  at  any 
rate  he  could  not  have  seen  the  star  reappear  with  sudden 
brightness  unless  the  dark  limb  was  undisturbed.  The 
same  occultation  was  observed  at  Waverly,  Sydney,  by 
Walter  F.  Gale,  under  fairly  good  conditions  and  thick 
haze.  With  a  six  and  a  quarter-inch  objective  and  magn. 
power  140  "the  disappearance  was  instantaneous  at  a 
notch  formed  in  the  Moon's  limb  by  two  peaks."  This 
description  of  the  point  of  ingress  indicates  that  the  limb 
of  the  Moon  was  steady  and  sharp. 

The  same  occultation  was  also  observed  at  Warrickville, 
near  Sydney,  by  C.  J.  Merfield,  with  a  seven  and  a  half- 
inch  reflector,  with  power  170.  "The  definition  was  fair, 
although  hazy  at  the  time  of  disappearance,  which  was  not 
instantaneous,  as  is  usual." 

Professor  Young,  in  his  "  General  Astronomy  "  (p.  246), 
refers  to  the  projection  of  a  star  on  the  Moon's  dark  limb 
in  the  following  paragraph:  "  In  some  cases  observers  have 
reported  that  a  star,  instead  of  disappearing  instantaneously 
when  struck  by  the  Moon's  limb  (faintly  visible  by  earth- 
shine),  has  appeared  to  cling  to  the  limb  for  a  second  or 
two  before  vanishing,  and  in  a  few  instances  they  have  even 
reported  it  as  having  reappeared  and  disappeared  a  second 
time,  as  if  it  had  been  for  a  moment  visible  through  a  rift 
in  the  Moon's  crust.  Some  of  these  anomalous  phenomena 
have  been  explained  by  the  subsequent  discovery  that  the  star 
was  double,  or  had  a  faint  companion."  No  further  explana- 
tion is  attempted.  We  have  purposely  watched  stars 
occulted  at  the  ash-gray  limb  of  the  Moon,  but  have  never 
been  able  to  see  a  sufficiently  bright  and  defined  limb  to 
note  whether  it  was  invaded  by  the  star  before  its  sudden 
disappearance. 

In  the  publications  of  the  Astronomical  Society  of  the 
Pacific  for  November  30,  1889,  Professor  Barnard,  of  the 
Lick  Observatory,  says  that  "  at  a  number  of  occultations 
of  the  satellites  [of  Jupiter]  I  watched  carefully  for  any 
evidences   of  their  being  seen   through  the    edges   of    the 


y 


9lj    J&ltrt^U-     I/a*^  £*~*rjA<*>GA  +fl**~Jfc     <£U/—&iAy 

/fat ,  /?}^rt6'  ■ 

78  'CALIFORNIA  ACADEMY  OF  SCIENCES         [Proc.  3d  Ser. 

planet,  but  saw  nothing  of  the  kind.  Professor  Holden 
informs  me,  however,  that  with  the  thirty-six-inch  Equa- 
torial the  whole  disc  of  a  satellite  has  been  visible  within 
the  planet's  atmosphere  at  every  occultation  he  has  ob- 
served." In  the  "Astronomical  Journal,"  volume  VIII, 
page  64,  there  is  a  record  by  these  observers  of  the  occul- 
tation of  47  Libras  (6.4  magn.)  by  Jupiter,  on  June  9,  1888. 
With  the  thirty-six-inch  objective  and  power  672,  the  images 
were  below  the  average  of  good  seeing.  Director  Holden 
reports  that  "the  star  entered  the  limb  and  was  seen 
bisected"  at  im  30s  after  it  had  touched  the  outer  edge. 
"  The  entire  image  of  the  star  was  seen,  inside  as  well  as 
outside  the  limb,  being  easily  distinguishable  from  the 
planet's  surface  by  its  brilliancy  and  peculiar  color."  In 
2m  g£8  <<  the  star  was  entirely  inside  the  limb,  but  still  vis- 
ible. For  the  next  ten  seconds  the  star  was  alternately 
visible  and  invisible,  and  the  planet's  limb  was  quite  un- 
steady." In  2m  51s  from  the  star's  first  touching  the  limb  it 
was  certainly  gone.  Professor  Barnard  observed  the  same 
occultation  with  the  twelve-inch  objective,  reduced  to  eight 
inches  because  "  the  images  were  too  unsteady  with  the 
full  aperture"  (magn.  power  240).  He  noted  the  time  of 
"  contact  of  the  following  edge  of  the  star  with  the  preced- 
ing limb  "  of  Jupiter.  At  im  12s  after )/Nhe  star  was  partly  on 
the  limb;  at  im  51s  the  star  was  seen  by  glimpses  to  that 
epoch,  and  three  seconds  later  it  had  certainly  disappeared 
when  it  had  advanced  about  three-quarters  of  its  disc  within 
the  limb.  On  the  usual  scale  of  seeing,  the  conditions  were 
below  the  average;  but  even  when  the  star  had  encroached 
on  the  limb  the  disc  was  small,  round  and  bright,  and  as 
clearly  defined  as  that  of  a  satellite  entering  transit.  No 
certain  diminution  of  its  light  was  observed. 

Professor  Barnard  makes  no  allusion  to  the  color  of  the 
star,  and  as  its  spectrum  is  recorded  as  that  of  the  first  type, 
there  seems  no  reason  why  the  first  mentioned  observer 
should  attribute  a  "  peculiar  color  "  to  it. 

Under  date  of  April,  1894,  Professor  Barnard  thinks 
"  astronomers  should  reject  the  idea  that  the  satellites  of 
Jupiter  can  be  seen  through  his  limb";    since,  under  good 


M.-P.— Vol.  I.]     DA  VIDSON— APPARENT  PROJECTION,  ETC.  79 

conditions,  with  the  Lick  thirty-six-inch  objective,  "  the  limb 
of  Jupiter  has  appeared  perfectly  opaque,  as  in  all  my  previous 
observations  with  smaller  telescopes."  But  he  makes  no 
reference  to  the  character  of  the  factitious  limb  of  the 
planet  in  unfavorable  conditions  of  the  atmosphere. 

At  Melbourne,  September  14,  1879,  the  occultation  of  64 
Aquarii  (6.9  magn.)  by  Jupiter  was  watched  in  the  great 
reflector.  The  star  was  thirty-five  seconds  in  disappearing, 
and  remained  visible  ten  seconds  longer  as  a  speck  of  light 
seen  through  ground  glass.  This  speck  "  also  disappeared 
gradually."  Proctor  says  the  observers  personally  assured 
him  the  phenomenon  was  not  due  to  irradiation. 

In  1878,  at  the  Adelaide  Observatory,  two  observers 
(Messrs.  Todd  and  Ringwood)  saw  the  occultations  of 
satellites  I,  II  and  III  upon  certain  occasions  "within  the 
disc  of  the  planet  "  at  disappearance,  and  once  at  reappear- 
ance. "  In  every  other  case  the  occultation  was  perfect  at 
the  limb."     This  latter  sentence  was  not  quoted  by  Proctor. 

Dr.  E.  C.  Pickering,  Director  of  Harvard  Observatory, 
has  described  an  occultation  of  D.  M.,  230  1087  (7.3  magn.), 
by  Jupiter,  April  14,  1883.  He  used  the  fifteen-inch 
objective,  with  achromatic  eye-piece,  power  400.  "  For  a 
period  of  about  ten  minutes  after  disappearance  was 
observed,  the  star  is  recorded  as  'suspected.'  The  record 
states  that  for  some  time  previous  to  final  disappearance 
'  the  star  alternately  disappeared  and  reappeared  without 
cause;  seeing  pretty  good  and  uniform  throughout.'  At 
the  reappearance,  the  limb  of  the  planet  was  watched  con- 
tinuously for  forty-nine  seconds,  at  the  beginning  of  which 
the  star  was  not  visible,  and  at  the  end  of  which  it  was  dis- 
tinctly seen,  remaining  visible  thereafter." 

In  our  experience  in  observing  Jupiter,  we  have  never 
seen  the  border  sharply  defined  when  using  powers  of  500, 
but  atmospheric  conditions  have  never  been  supremely 
good  at  the  times  of  observation.  In  observing  the  occul- 
tation of  Jupiter's  satellites  through  an  unsteady  atmosphere, 
our  fellow-observer,  with  a  smaller  telescope  and  objective 

(  2  )  November  19,  1900. 


J 


80  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

of  two  and  one-half  or  three  inches,  lost  the  satellite  much 
sooner  than  we  observed  its  disappearance  in  the  6.4-inch 
Clark  Equatorial,  when  we  followed  it  into  the  factitious 
limb ;  and  with  a  disturbed  atmosphere  this  advantage  should 
always  pertain  to  the  larger  objective  and  higher  power. 

Numerous  observers  might  be  quoted  who  have  seen 
stars  and  satellites  projected  within  the  apparent  limb  of 
Jupiter  at  occultation.  Some  of  the  details  are  rather 
startling,  and  perhaps  the  most  notable  is  that  by  Admiral 
Smyth,  in  1828,  supported  in  part  by  two  other  observers 
at  stations  a  few  miles  distant.  The  satellite  II  remained 
for  some  minutes  projected  upon  the  apparent  edge  of  the 
planet,  and  thirteen  minutes  afterwards  it  was  outside  of  the 
disc;  then  it  remained  visible  four  minutes  and  "  suddenly 
vanished."  If  the  observers  had  been  experts,  observing 
with  instrumental  means  adequate  to  give  sufficient  light, 
definition,  and  size  to  the  images  —  noting  the  times  with 
accuracy,  and  fully  recognizing  the  effect  of  the  locally 
disturbed  atmosphere  —  we  are  satisfied  that  some  satisfac- 
tory explanation  would  have  been  reached. 

Such  details  as  these,  and  others  upon  different  occa- 
sions, are  rather  astonishing.  Such  remarkable  conditions 
must  be  due  to  imperfect  instrumentation,  to  inexperience, 
to  weariness  or  lack  of  quick  and  positive  accommodation 
of  the  eye,  to  erroneous  estimates  of  small  intervals  of  time, 
to  extraordinarily  abnormal  conditions  of  the  atmosphere,  to 
intervals  of  unconscious  cerebration,  or  to  gross  mistakes. 
It  was  from  the  abnormal  observations  at  Melbourne  that 
Proctor  undertook  to  deduce  the  depth  of  Jupiter's  atmo- 
sphere, and  concluded  that  the  star  64  Aquarii  was  seen 
through  a  range  of  10,000  miles  of  atmosphere  below  a 
depth  of  300  miles. 

We  may  here  mention  incidentally  that  for  many  years  we 
have  been  on  the  outlook  for  Saturn  and  his  ring  system  to 
occult  some  star  of  moderate  magnitude;  but  the  phenome- 
non has  not  occurred  in  our  experience.  We  were  anxious  to 
learn  how  the  ring  system  would  treat  the  star. 


M.-P.— Vol.  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.  8l 

Similar  Phenomena  at  Total  Solar  Eclipses.  ' 

Many  reports  of  observations  of  total  solar  eclipses  and 
transits  of  Venus  and  of  Mercury  over  the  Sun's  disc  are 
painfully  discordant,  misleading  and  uninstructive.  They 
betray  inexperience  and  lack  of  knowledge  of  the  local 
physical  disabilities  that  may  present  themselves.  It  would 
almost  appear  as  if  those  who  had  the  least  experience  were 
the  most  authoritative  in  their  opinions.  And  certainly, 
when  the  results  are  published,  there  is  little  or  no  discrim- 
ination made  in  assigning  proper  weights  to  them.  Some 
observers  make  no  mention  of  their  defective  eyesight,  and 
♦  we  have  personally  known  observers,  quoted  as  authority, 
that  should  never  have  been  trusted  to  attempt  any  observa- 
tion of  precision. 

The  elaborate  reports  of  the  total  solar  eclipse  of  1869. 
in  the  United  States,  by  many  observers  in  different  locali- 
ties, are  quite  instructive  in  the  unconscious  exhibition  of 
contradictory  statements  and  inappropriate  adjectives.  Two 
observers  at  the  same  station  reported  directly  opposite 
conditions  of  the  steadiness  of  the  limbs  of  the  Sun  and 
Moon.  One  said  they  were  defined  with  the  utmost  clear- 
ness; another  sent  us  drawings  to  explain  his  statement  that 
they  were  "boiling  excessively."  And  yet  the  observer 
who  reported  steadiness  was  in  doubt  twelve  seconds  of 
the  time  of  contact,  and  took  the  mean  of  his  limits  of 
doubt.  And  it  is  evident  that  the  many  observers  had  dif- 
ferent conceptions  of  what  constituted  the  phenomenon  of 
"  Baily's  beads."  Some  looked  for,  and  evidently  ex- 
pected, the  exhibition  as  a  necessary  and  normal  physical 
condition.  The  tabulated  descriptions  of  the  phenomena 
at  totality  range  wildly;  we  find  recorded:  "no  trace  of 
Baily's  beads;"  "the  phenomenon  of  Baily's  beads  lasted 
but  a  few  moments;"  "Baily's  beads  beautifully  distinct 
and  spreading  over  an  arc  of  300;"  "Baily's  beads  were 
seen  fifteen  seconds  or  more;  they  were  long  and  thin, 
moved  with  the  moon,  and  were  unquestionably  the  effect 
of  the  irregularities  of  the  Moon's  contour  exaggerated  by 


82  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

irradiation."  One  observer  has  given  detailed  drawings  of 
the  form  of  the  "beads,"  and  exhibits  them  with  mechan- 
ical precision  and  hardness;  as  a  matter  of  fact  he  was  not 
a  draughtsman  nor  a  skilled  observer,  and  yet  his  name 
carried  great  weight.    Ci,  v Oi  *  VoV-J^ 

Similar  Phenomena  at  Transits  of  Venus  and  Mer- 
cury across  the  Sun's  Disc 

In  our  observations  of  the  transit  of  Venus,  December 
1882,  at  Cerro  Roblero,  New  Mexico,  5,676  feet  above  the 
sea,  and  1,655  ^eet  above  the  Rio  Grande  del  Norte  and  the 
great  arid  plain  of  the  Jornado  del  Muerte,  there  were, 
towards  the  close,  occasional  tremors  or  shiverings  of  the 
borders  of  the  discs  of  the  Sun  and  planet  from  slight 
tremulousness  of  our  atmosphere;  but  the  eye  was  not  con- 
fused, as  would  have  been  the  case  if  the  discs  had  con- 
tinued ill-defined  and  unsteady  by  excessive  vibration.  In 
the  first  case  the  eye  could  and  did  select  its  opportunity 
for  micrometric  measurements.  But  at  this  very  period  the 
assistant  astronomer  in  charge  of  the  photographic  expo- 
sures reported  the  results  unfavorably  affected  by  this 
slight  unsteadiness.  It  was  a  case  where  the  eye  selected 
a  moment  of  steadiness,  but  the  mechanical  movement  of 
the  photographic  shutter  permitted  no  selection.  The  un- 
steadiness of  the  atmosphere  at  the  time  between  the  third 
and  fourth  contacts  permitted  a  beautiful  and  unique  exhi- 
bition of  the  fine,  white,  faint,  crescent  of  coronal  light 
apparently  surrounding  part  of  the  disc  of  Venus  as  an  illu- 
minated atmosphere.  The  crescent  was  long,  extremely 
thin,  white,  and  as  fine,  sharp  and  regular  as  if  cut  by  the 
finest  graver;  and  we  watched  it  die  away  in  excessive  mi- 
nuteness. We  made  drawings  of  the  exhibition.  Another 
observer  of  this  beautiful  phase  of  the  transit  at  a  different 
station  saw  a  similar  phenomenon  "shortly  after  the  first 
external  contact,  when  the  limb  of  the  planet  was  'boiling," 
and  "it  was  difficult  to  be  certain  whether  it  lay  within  or 
without  the  planet's  contour  *  *  *  but  it  certainly  ap- 
peared to  extend  at  any  rate  within  the  circumference;   and 


M.-P.— Vol.  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.  83 

indeed  it  presented  the  appearance  of  'Baily's  beads'  at 
the  time  of  a  total  solar  eclipse.  Its  whole  depth  was  one- 
fourth  of  the  planetary  radius";  and  the  published  drawing 
showed  the  broader  part  of  the  coronal  light  partly  inside 
the  planet's  circumference  when  the  planet  was  half  on  the 
Sun's  disc.  Astr.  Nach.  2,481.  Here  we  have  exhibitions 
of  the  same  or  a  similar  phenomenon  at  the  same  transit 
under  widely  different  atmospheric  conditions;  and  the  first 
is  surely  to  be  taken  as  better  representing  the  true  or  nor- 
mal phase  of  the  phenomenon,  and  the  latter  is  to  be 
reckoned  as  abnormal  and  misunderstood. 

This  phenomenon  of  the  so-called  "  atmosphere  of 
Venus,"  though  not  connected  with  the  disturbance  of  our 
atmosphere,  is  thus  seen  to  be  affected  by  it  just  as  much  as 
the  outline  of  Sun  or  planet.  Mouchez  has  called  it  the 
"pale  aureole  *  *  *  to  be  attributed  in  part  to  the  at- 
mosphere of  the  Sun  rendered  visible  by  contrast,  and  also 
in  part  by  the  atmosphere  of  Venus."  Heraud  and  Bonify 
designated  it  as  the  "filet  lumineuse;"  and  Airy  says  this 
"penumbra  must,  of  course,  be  considered  a  part  of 
Venus;"  and  elsewhere  he  says  "the  partial  illumination  of 
the  atmosphere  of  Venus  introduces  difficulties  of  observa- 
tion" etc.  One  observer  says  that  this  ring  of  light  around 
Venus  enabled  him  to  see  the  planet  twenty-four  minutes 
before  contact.  One  of  our  astronomers  who  had  wit- 
nessed the  transits  of  Venus  of  1874  a°d  z882  asserts  that 
"there  seems  to  be  absolutely  no  way  of  escaping  from  a 
new  difficulty — the  planet's  atmosphere  causes  it  to  be  sur- 
rounded by  a  luminous  ring — as  it  enters  upon  the  Sun's 
disc,  and  thus  renders  the  time  of  contact  uncertain  by  at 
least  five  or  six  seconds."  Another  admits  "the  disturb- 
ance of  the  image  by  irregular  refraction  in  the  Earth's 
atmosphere,"  but  declares  that  "we  must  look  to  the  chief 
cause  of  the  great  discordances"  of  the  times  of  contact  of 
Venus  and  the  Sun,  "in  the  atmosphere  which  surrounds 
Venus."  And  he  further  says,  that  "the  cruel  manner  in 
which  all  the  phenomenon  are  modified  by  the  atmosphere 
of  Venus  is  not  easy  to  explain."     Another   declares   "the 


84  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

planet  was  surrounded  by  a  ring  of  light,  as  bright  as  the 
Sun,  that  pushed  the  edge  away  from  it;  and  no  actual  con- 
tact could  be  observed."  And  yet  there  was  no  black  drop, 
no  ligament  and  no  distortion  reported  by  the  observer. 

It  is  admitted  that  there  is  no  atmosphere  enveloping 
the  Moon,  and  yet  Royal  Astronomer  Stone  at  the  Cape  of 
Good  Hope  observed  the  outline  of  the  Moon  projected 
against  the  Sun's  corona  five  minutes  and  eight  seconds 
before  the  total  phase  of  a  solar  eclipse.  We  reported  a  very 
faint  exhibition  of  this  phenomenon  January  nth,  1880. 
If  the  corona  of  the  Sun  is  the  visible  arc  of  illumination  in 
this  case  through  contrast,  we  are  entirely  justified  in  as- 
suming it  to  be  the  agent  of  illumination  at  the  circumfer- 
ence of  Venus;  and  on  account  of  the  irregularity  and 
inequality  of  the  brightest  parts  of  the  corona,  it  may  be 
seen  at  one  part  of  the  planet's  circumference  and  not  at 
another,  or  it  may  be  seen  all  around  the  planet.  A  critical 
examination  of  the  reports  clearly  demonstrates  that  this 
faint  illumination  on  the  border  of  the  dark  body  of  the 
planet  is  seen  as  (1)  part  of  a  circumference;  (2)  at  dif- 
ferent parts  of  the  circumference;  (3)  of  varying  breadth 
at  different  points  of  its  length  by  the  same  observer;  (4) 
as  wholly  encircling  the  planet.  If  it  were  the  atmosphere 
of  Venus  it  would  be  uniform  and  continuous,  unless  a 
Venus  cloud  system  interfered  irregularly.  Professor 
Young  says  (p.  159)  that  at  a  total  solar  eclipse  there  is 
"not  any  ring  of  light  running  out  on  the  edge  of  the  Moon 
like  that  which  encircles  the  disc  of  Venus  at  the  time  of 
the  transit." 

With  a  slight  digression,  we  mention  one  or  two  vagaries 
of  observers  of  the  transits  of  Mercury. 

At  one  of  the  recent  transits  where  the  observers  were 
side  by  side,  one  reported  the  "definition  of  Mercury  sharp 
and  steady,"  and  the  "limb  of  the  Sun  undulating,"  as  if  the 
two  objects  were  unequally  affected.  The  other  observer 
described  the  "limbs  of  the  Sun  and  Mercury  loosely  con- 
nected by  a  patch  of  haziness  oscillating  between  them;" 
and  at  another  phase  the   "undulations   of  the    Sun's  limb 


M.-P— Vol.  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.  85 

occasionally  reached  Mercury;"  leaving  the  inference  that 
the  planet  was  steady.  At  yet  another  station  the  "planet 
appeared  with  rippling  fiery  and  black  balls  chasing  each 
other  between  the  planet  and  the  Sun."  In  the  transit  of 
1878  one  observer  "was  surprised  at  the  absence  of  glare 
and  tremor;  and  the  edge  of  the  Sun's  disc  was  clearly  de- 
fined and  remarkably  steady  with  the  exception  of  a  few 
notches  and  scratches." 

We  had  been  fortunate  in  our  observations  of  the  two 
transits  of  Venus,  and  of  several  transits  of  Mercury,  never 
to  have  seen  an  exhibition  of  "black  drop"  or  "ligament," 
except  at  the  transit  of  Mercury  in  1891,  when  the  atmos- 
pheric conditions  of  San  Francisco  were  very  unfavorable 
although  the  sky  was  clear;  the  limbs  of  the  Sun  and 
planet  were  both  spurious  or  factitious  on  account  of  exces- 
sive vibration;  and  the  observation  was  necessarily  difficult 
and  doubtful.  Under  such  adverse  conditions  the  observa- 
tion may  be  very  wild,  or  it  may  turn  out  very  good;  but 
certainly  the  observer  cannot  assign  much  weight  to  the 
epoch  noted. 

Instructions   for  Observing  the   Transit  of  Venus. 

In  re-examining  the  large  number  of  reports  of  the  transits 
of  Venus  of  1874  an(^  1882,  we  have  gathered  forty  or 
fifty  expressions  of  the  observers  in  their  endeavors  to  de- 
scribe the  phenomenon  usually  known  as  "black  drop," 
"ligament,"  or  "filament." 

This  need  hardly  be  wondered  at.  The  British  Instruc- 
tions of  1882  assert  that  the  phenomena  seen  by  most  ob- 
servers near  the  time  of  contact  are  of  a  complex  character, 
and  extend  over  considerable  intervals  of  time.  These  in- 
structions surely  conveyed  the  impression  that  these  complex 
phenomena  were  the  normal  physical  conditions.  They 
added  confusion  to  previous  descriptions  by  mention  of  the 
"light  of  the  cusps;"  and  evidently  regarded  the  exhibition 
of  haze,  or  ligament,  as  "the  glimmering  of  the  light  of  the 
'aureole,'   'penumbra',  or  'sunlight'  refracted  through  the 


86  CALIFORNIA  ACADEMY  OF  SCIENCES.       [Proc.  3D  Ser. 

atmosphere  of  Venus  across  the  dark  space  between  the 
cusps."  And  further,  if  a  "pure  geometrical  contact"  (which 
is  the  only  line  that  can  be  given  for  contact)  is  frustrated  by 
haze,  shadow,  ligament,  or  black  drop,  then  the  last  marked 
discontinuity  of  the  illumination  of  the  Sun  near  the  point  of 
contact  is  the  epoch  to  be  recorded  if  it  "is  distinctly  recog- 
nized as  independent  of  mere  atmospheric  tremor." 

The  American  Instructions  were  mainly  based  upon  the 
appearances  of  1769;  and  declared  the  "atmosphere  of 
Venus  clearly  illuminated."  They  refer  to  the  difficulty  of 
observing  the  moment  of  tangency  on  account  of  imperfec- 
tion of  vision,  irradiation  produced  by  the  Earth's  atmos- 
phere, and  imperfections  in  the  telescope;  and  then 
mention  the  difficulties  to  be  expected  by  atmospheric 
undulation. 

One  of  our  eminent  astronomers  accepts  the  explanation 
of  Lalande,  that  the  phenomenon  of  "black  drop,"  etc.,  is 
caused  by  irradiation  at  the  bright  object;  and  that  this  irra- 
diation arises  from  a  number  of  causes,  imperfections  of  the 
eye,  imperfections  of  the  telescope,  and  the  softening  effect 
of  the  atmosphere  upon  a  celestial  object  when  seen  near 
the  horizon.  He  likens  it  to  a  narrow  and  less  bright  false 
edge  around  the  bright  object;  and  says  that  this  band  will 
appear  narrower  the  better  the  telescope  and  the  steadier 
the  atmosphere.  He  furthermore  says  that  in  the  observa- 
tions of  the  transit  of  Venus  of  1874,  with  the  improved 
instruments,  very  few  of  the  experienced  observers  no- 
ticed any  distortion  at  all.  Later  on  he  adds  that  "in  the 
varied  forms  presented  'when  the  air  is  not  still,'  we  recog- 
nize all  the  peculiar  appearances  described  by  the  observers 
of  1769."  In  1874  tne  Mexican  observers  at  Yokohama 
reported  to  us  a  decided  exhibition  of  "black  drop." 

Colonel  Tennant  has  remarked  of  the  black  drop  phenom- 
enon, "  there  is  no  doubt  in  my  mind  that  the  outer  part  of 
the  Sun  is  never  free  from  the  result  of  outstanding  astigma- 
tism." We  have  astigmatism  of  the  human  eye,  and  astig- 
matism of  the  telescopic  objective  and  ocular,  but  we  do 
not  understand  to  which  he  applies  the  term,  if  to  either  of 


M.-P.—  Vol.  L]     DAVIDSON— APPARENT  PROJECTION,  ETC.  87 

them.  And  one  of  our  best  astronomers,  in  reviewing  the 
physical  and  other  conditions  of  the  1761,  1769  and  1874 
transits,  summed  up  his  deductions  by  saying  that  "  the 
black  drop,  and  the  atmospheres  of  Venus  and  the  Earth, 
had  again  produced  a  series  of  complicated  phenomena 
extending  over  many  seconds  of  time." 

Curious  Descriptions  of  the  Phenomena. 

With  much  more  speculation  of  similar  import  we  should 
be  prepared  for  the  crude  descriptions  and  attempted  ex- 
planations given  by  the  observers.  They  range  from 
a  'Chinaman's  hat'  to  a  'pear-shaped  planet,'  and  are  even 
stretched  out  to  a  'gourd  shape.'  The  descriptions  and  ex- 
planations by  the  same  observer  are  sometimes  curiously 
contradictory  or  vague,  as:  'the  limbs  were  boiling  vio- 
lently,' 'yet  quite  sharp  and  doubt  only  three  or  four 
seconds;'  there  was  'black  drop'  but  'no  distortion;'  'no 
distortion'  yet  the  'limbs  of  the  Sun  and  Moon  were  spin- 
ning;' '  interference  lines;'  '  Venus  serrated;'  'the  Sun's 
limb  had  lost  its  sharpness  from  the  overlapping  of  Venus' 
atmosphere;'  the  '  shadow  of  contact;'  from  the  overlap- 
ping of  the  two  'penumbras  of  imperfect  definition;'  and 
most  remarkable  and  incomprehensible,  '  the  sympathetic 
attraction  or  assimilation '  of  the  limbs  of  the  Sun  and  the 
planet  at  the  second  contact  but  no  'mutual  attraction'  at  the 
third. 

In  Egypt,  in  1882,  one  observer  paid  particular  attention 
to  detect  the  black  drop  and  could  not  see  it;  another  ob- 
server at  the  same  locality  observed  the  black  drop.  The 
imagination  would  seem  to  have  played  a  part  in  the  obser- 
vations. One  observer  saw  Venus  twenty-four  minutes 
before  contact;  and  near  the  first  contact  he  saw  "a  dis- 
tinct cone  of  shadow  thrown  away  into  space;"  and  his 
drawing  is  stronger  and  stranger  than  his  description.  In 
1874  *he  chief  astronomer  of  one  of  the  foreign  expeditions 
declared  to  us  that  the  phenomenon  was  simply  and  solely  a 
case  of  diffraction. 


88  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

Errors  of  Observation. 

It  is  therefore  astonishing  to  note  that  under  such  adverse 
conditions  for  accurate  observation  the  times  of  contacts 
are  noted  to  tenths  of  seconds.  As  two  seconds  of  time 
mark  the  apparent  relative  movement  of  the  bodies  about 
one-tenth  of  a  second  of  arc,  we  need  not  wonder  that  some 
of  the  observers  were  not  sure  of  the  minute;  and  in  one 
case  an  error  of  three  minutes  could  not  be  fixed.  This 
occasional  and  accidental  distortion  of  the  planet's  disc 
in  such  transits  had  called  for  the  determination  of  the 
epoch  of  the  geometrical  contact  of  the  limbs  of  the  images 
of  the  two  bodies  and  for  other  appearances ;  but  under 
such  unfavorable  conditions  the  judgment  of  the  best  ob- 
server may  reasonably  have  been  at  fault,  and  his  recorded 
epoch  of  contact  very  wild.  This  is  shown  by  many  illus- 
trations of  the  distortion  where  the  outlines  of  the  "black 
drop"  are  drawn  with  a  hardness  and  positiveness  that  are 
certainly  uninstructive,  and  unsuggestive  of  the  cause. 

The  difficulty  of  observation  is  made  painfully  manifest 
in  the  experiments  at  Washington  early  in  1874,  when  most 
of  the  observers  practised  upon  an  artificial  transit  of 
Venus  to  determine  the  times  of  the  four  contacts.  The 
observations  range  from  four  seconds  before  the  first  con- 
tact to  twenty-eight  seconds  after;  and  even  at  the  second 
and  third  contacts,  from  twenty-one  seconds  before  to  sev- 
enteen seconds  after  the  epochs.  These  extraordinary  per- 
sonal equations  must  surely  have  been  due  in  part  to  inex- 
perience, and  mainly  to  the  disturbed  conditions  of  the  at- 
mosphere. And  yet  the  mean  value  of  a  series  of  such 
observations  was  applied  to  the  actual  observations  in 
the  field  upon  the  Sun  and  planet,  to  reduce  them  to 
a  systematic  series.  Had  these  preliminary  observations 
been  made  in  a  serene  atmosphere,  the  apparent  per- 
sonal equations  would  have  been  brought  to  normal  and 
reasonable  limits,  notwithstanding  one  observer  declares 
that  "the  optical  edge  of  a  bright  body  is  not,  and  in  the 
nature  of  things,  cannot  be,  absolutely  sharp  in  the  eye  or 
in  the  telescope."     The  great  discrepancies  arose  in  large 


M.-P.— Vol.  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.  89 

measure  from  the  unsteadiness  of  the  short  line  of  inter- 
vening atmosphere  near  the  ground;  and  we  then  related 
our  experience  at  great  elevations  and  over  heated  plains, 
and  urged  the  occupation  of  elevated  and  isolated  stations 
as  the  most  effective  means  of  avoiding  an  unsteady  atmos- 
phere in  such  costly  and  important  observations. 

Observations    of    Solar   Eclipses    under    Different 
Atmospheric    Conditions. 

Professor  Dr.  Schaeberle  of  the  Lick  Observatory  ob- 
served the  total  solar  eclipse  of  October  9,  1893,  at  6,600 
feet  elevation,  on  the  western  flank  of  the  Andes  in  Chili. 
He  was  eminently  successful  in  all  his  observations  on  ac- 
count of  the  extreme  steadiness  of  the  atmosphere.  The 
Sun's  image,  projected  by  the  six-inch  equatorial  upon  a 
white  cardboard,  looked  "more  like  an  engraving  than  an 
optical  image."  Aubertin,  at  the  same  station,  said  that 
during  the  eclipse  "the  atmosphere  was  absolutely  pellu- 
cid"; he  had  had  experience  at  Gibraltar  in  1870. 

Our  experience  in  observing  the  above  eclipse  at  San 
Francisco  as  a  partial  phase  was  the  reverse  of  Professor 
Schaeberle's,  but  very  instructive.  We  condense  the  report. 
The  images  of  the  Sun,  and  the  micrometer  thread  were 
projected  by  the  6.4-inch  equatorial  upon  a  white  sheet  of 
paper.  The  apparent  diameter  of  the  Sun's  image  was 
about  twenty-two  inches.  The  atmosphere  was  unsteady, 
and  the  border  of  the  Sun  was  confused  and  blurred,  and 
lacked  the  solid  or  consistent  brightness  of  the^disc.  This 
factitious  border  was  about  half  a  millimeter  broad  at  the 
least.  The  solar  spots  were  confused  and  their  details  were 
not  distinguishable.  As  the  time  of  first  contact  approached 
we  watched  the  predicted  point  of  contact,  not  for  the  first 
indentation  of  the  Sun's  disc,  but  for  the  first  commingling 
or  overlapping,  so  to  speak,  of  the  factitious  image  of  the 
Moon's  border  with  the  factitious  image  of  the  Sun's  border. 
There  first  appeared  a  very  faint  darkening  of  the  confused 
and  apparently  expanded  border  of  the  Sun's  limb.  We 
noticed  it  when  it  was  about  three   millimeters  long;    the 


90  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

disturbance  of  the  limb  was  very  great.  The  dark  com- 
mingling or  overlapping  increased  in  length,  breadth,  and 
darkness;  and  at  last  changed  to  a  line  of  blackness  when 
the  actual  limb  of  the  Moon's  image  touched  upon  the  Sun's 
condensed,  brighter  and  actual  border.  There  was  no 
hesitation  in  noting  the  time  of  this  contact  by  several 
observers.  At  the  time  of  the  last  contact,  four  of  the 
observers  watched  the  phenomenon.  The  borders  of  the 
two  discs  were  more  unsteady  than  at  the  first  contact,  and 
the  reversed  order  of  the  first  contact-appearances  took 
place.  A  great  mountain  range  of  the  Moon  was  the  last 
to  disappear.  The  two  exhibitions  were  very  instructive. 
At  the  total  solar  eclipse  of  January  11,  1880,  on  the 
Sierra  Santa  Lucia,  6,100  feet  above  the  sea,  we  observed 
the  phenomenon  under  peculiar  circumstances  fully  detailed 
in  the  official  report.  The  atmosphere  was  beautifully 
serene  after  a  prolonged  and  terrific  storm  of  wind  and 
snow.  The  limb  of  the  Sun  was  not  absolutely  steady  but 
exhibited  occasional  tremors  or  shiverings,  and  there  was  no 
disturbance  of  the  limb  at  first  contact.  "  The  cusps  were 
very  sharp  and  clear,  and  whenever  a  tremor  occurred  on 
account  of  any  slight  atmospheric  disturbance  these  cusps 
were  apparently  doubled."  (At  Oakland  where  the  atmos- 
phere was  much  disturbed  the  cusps  appeared  confused  and 
blunted.)  As  totality  approached,  the  crescent  of  the  Sun 
was  remarkably  long  and  narrow  on  account  of  the  slight 
difference  of  the  apparent  semi-diameters  of  the  Sun 
(16'  18". 1)  and  the  Moon  (16'  23"  .5).  The  last  line  of  the 
crescent  was  300  to  400  long  before  it  broke.  It  exhibited 
no  distortion  from  atmospheric  disturbances  except  an  occa- 
sional tremor  or  shivering.  The  cusps,  before  the  crescent 
was  reduced  to  a  line,  were  remarkably  sharp,  curved  points, 
as  if  cut  by  the  finest  graver.  The  breaking  of  this  last 
thin  line  of  sunlight  was  occasioned  by  the  intrusion  of  the 
lunar  mountains  and  the  inequalities  of  outline.  It  pre- 
sented the  appearance  of  a  line  of  bright  dots  and  dashes, 
and  black  spaces.  There  was  no  wavy  motion  to  interfere 
with    this    exhibition;     whenever    a    bright    spot    or  a  line 


M.-P.— Vol.  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.  91 

disappeared  it  was  instantaneous,  and  gone  forever.  The 
moving  dots  of  the  "  Baily's  beads"  were  absolutely 
wanting.  At  the  last  contact  of  the  eclipse  the  atmospheric 
conditions  were  wholly  changed.  The  atmosphere  was  in 
a  remarkable  state  of  undulation  and  the  limbs  of  the  Moon 
and  Sun  were  moving  in  great  rapid  waves,  and  the  obser- 
vation was  unsatisfactory.  The  Sun  set  below  the  ocean 
horizon  about  ten  minutes  later  and  we  should  have  ex- 
pected a  quiet  atmosphere,  but  the  warm  Sun  rays  heating 
the  air  upon  the  steep,  snow-covered  ocean-side  of  the 
mountain  mass  caused  rapid  evaporation  of  the  snow,  and 
irregularly  heated  currents  of  air  to  flow  over  the  station. 
At  this  eclipse  we  called  attention  to  the  less  darkness  of  the 
sky  adjacent  to  the  advancing  body  of  the  Moon,  due  to 
contrast  with  coronal  effects. 

At  the  solar  eclipse  of  October  30,  1883,  we  projected 
the  images  of  the  Sun  and  Moon  upon  a  sheet  of  white 
paper,  and  studied  the  disturbed  outline  of  both  objects. 
The  greatest  obscuration  occurred  just  before  sunset,  when 
the  Moon  was  half  way  over  the  Sun's  disc.  Owing  to  the 
extreme  refraction  at  this  zenith  distance,  and  the  "exceed- 
ingly great  boiling"  of  the  borders  of  the  two  images,  the 
"distortion  of  the  cusps  was  striking  and  peculiar." 

In  contrast  with  these  two  exhibitions  of  great  atmospheric 
unsteadiness,  we  introduce  an  experience  approaching  that 
of  Professor  Schaeberle's  above  mentioned.  , 

We  observed  the  total  solar  eclipse  of  August  7,  1879,  on 
the  Chilkaht  River  in  Alaska,  near  the  end  of  heavy,  cloudy 
weather,  when  the  atmosphere  had  become  clear  and  steady. 
At  the  first  contact  "the  limb  of  the  Moon  was  very  sharply 
defined,  and  the  outline  of  the  Sun  was  very  steady  and 
sharp."  Just  before  totality  "the  crescent  was  very  beauti- 
ful to  the  unassisted  eye,  and  in  the  telescope."  In  the 
three-inch  Fraunhofer,  with  moderate  power,  the  "borders 
of  the  Sun  and  Moon  were  remarkably  steady  and  very 
sharply  defined.  In  twenty-four  years  of  practice  in  observ- 
ing we  have  rarely,  if  ever,  seen  them  under  such  favor- 
able circumstances.     We  observed  them  without  any  shade , 


92  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Skr. 

and  followed  the  Sun's  border  to  the  instant  of  disappear- 
ance. The  bright,  long,  narrow  crescent  was  sharply  and 
regularly  defined  throughout;  the  •extremities  were  clear- 
cut  and  pointed.  As  the  width  and  length  of  the  crescent 
decreased,  this  sharpness  of  outline  and  regularity  of  form 
were  maintained  until  it  became  a  fine  line  of  living  white  j 
and,  shortening  rapidly,  it  disappeared  as  a  very  short,  fine, 
distinct  line,  and  not  as  a  star  at  its  disappearance.  There 
was  no  breaking  of  this  line  into  points  or  heads;  no  wave 
motion  along  it;  no  disturbance  whatever  of  continuity  or 
regularity  of  form . ' ' 

"A  feature  of  the  phenomenon  of  totality  was  the  vivid 
impression  that  the  dark  body  of  the  Moon  stood  out  clearly 
and  unmistakably  in  relief  in  the  space  between  the 
observer  and  the  coronal  brightness  around  the  obscured 
body  of  the  Sun,  and  did  not  lie  flat  and  upon  it,  as  in  a 
picture."  This  perspective  effect  resulted  from  the  seren- 
ity of  the  atmosphere,  the  sharpness  of  the  Moon's  outline, 
and  an  impression  that  the  dark  Moon  was  very  close  to  us. 

Graphic  Exhibitions  of  Unsteadiness. 

If  it  were  necessary  to  add  graphic  demonstration  to  the 
effect  of  the  disturbed  atmosphere  already  described,  we 
have  it  in  the  photographs  referred  to  in  the  following  note 
by  Warren  de  la  Rue,1  where  he  describes  the  method  of 
photographing  the  Sun's  disc,  in  a  very  small  fraction  of 
a  second.  He  says,  "So  rapid  is  the  delineation  of  the 
Sun's  image  that  fragments  of  the  limb,  optically  detached 
by  the  '  boil '  of  our  atmosphere,  are  frequently  depicted 
on  the  collodion,  completely  separated  from  the  remainder 
of  the  Sun's  disc;  more  frequently  still  from  the  same 
cause  the  contour  of  the  Sun  presents  an  undulating  line." 
To  this  case  can  be  added  a  photograph  of  the  Sun  taken  at 
the  Lick  Observatory  January  14,  1897;  wherein  the  facti- 
tious limb  is  like  a  nocculent  border  of  cotton  or  wool  with 
ragged  holes  through  the  relatively  faint,  irregular  outline 

1  Proc.  Brit.  Assn.  Adv't.  Sci.,  Aberdeen,  1859,  page  151. 


M.-P.— Vol.  L]     DAVIDSON— APPARENT  PROJECTION,  ETC.  93 

of  the  disc;  and  several  cloud-like  areas  actually  detached. 
The  breadth  of  the  thin  border  is  about  6",  and  the  whole 
factitious  breadth  must  be  more. 

It  seems  a  physical  impossibility  that  we  should  be  able 
to  detect  any  irregularities  of  even  a  dense  atmosphere  at 
the  border  of  the  Sun.  If  that  body  were  to  decrease  45 
miles  in  diameter,  our  instrumentation  would  not  be  able  to 
measure  it  under  present  conditions.  Much  less  could  we 
detect  it  if  there  were  actually  rolling  billows  of  the  exterior 
matter  of  the  Sun  45  miles  high  around  its  border.  They 
would  subtend  but  0.1"  in  height;  a  quantity  covered  by  the 
finest  spider  thread  in  the  telescope.  Much  less  could  we 
detect  any  changes  of  atmospheric  conditions  at  the  dis- 
tances of  Jupiter,  Mars,  Venus,  or  Mercury.  Some  great 
deep  Sun  spot  just  on  the  edge  of  the  Sun  would  doubtless 
show  a  depression,  but  not  any  imaginable  storm  disturbance 
of  the  densest  atmosphere,  as  we  understand  storms  and 
waves. 

Official  Recognition  of  the  Factitious  Borders  of 
the  Moon  and  Sun. 

In  still  further  confirmation  of  the  existence  of  the 
spurious  limbs  of  the  Moon  and  Sun  under  unfavorable 
atmospheric  conditions,  it  is  only  necessary  to  appeal  to  the 
representative  of  astronomical  authority  in  the  American 
Ephemeris  or  Nautical  Almanac.  In  that  government  pub- 
lication an  empirical  correction  of  2". 5  is  applied  to  the 
Moon's  semi-diameter  in  order  to  represent  the  observed 
value  in  meridian  instruments.  But  this  "  constant  is 
omitted  in  the  computation  of  solar  eclipses  and  occultations 
as  due  to  telescopic  and  ocular  irradiation"  (p.  528, 
1899).  This  2". 5  of  increased  semi-diameter  may  represent 
the  average  measure  of  the  factitious  border,  but  certainly 
it  is  frequently  much  greater. 

In  many  years  of  experience  upon  the  Pacific  Coast  of 
the  United  States  in  observing  lunar  transits,  we  have 
learned  to  expect  wild  results  when  a  markedly  factitious 
bright  limb  of  the  Moon  was  observed,  the  resulting  longi- 
tude being  always  affected  as  if  the  diameter  of  the  Moon 


94  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

were  too  great.  At  times,  when  the  vibration  or  undulation 
of  the  disc  of  the  Moon  was  not  rapid,  the  sharp,  solid 
limb  could  be  observed  even  with  a  faint,  spurious,  vibrat- 
ing outline  beyond  it.  In  i889-'90,  during  lunar  transit 
observations  for  longitude  at  San  Francisco,  our  party  had  a 
case  of  spurious  disc  from  excessive  diffusiveness,  with  a  pre- 
dicted error  in  the  resulting  longitude  that  was  verified 
upon  reduction.  This  clearly  indicated  that  even  the  offi- 
cial empirical  correction  may  frequently  be  too  small; 
while  in  times  of  supreme  steadiness  of  the  atmosphere  and 
resulting  sharpness  of  the  limb  of  the  Moon,  this  correction 
is  not  required. 

If  this  factitious  diameter  belongs  to  the  Moon,  the  Sun 
is  much  more  likely  to  carry  a  more  pronounced  factitious 
diameter,  and  every  observer  must  have  frequently  watched 
its  wildlv  boiling  limb  flaring  and  leaping  across  the  threads 
or  rolling  forward  like  waves  of  flame  along  the  horizontal 
thread.  This  factitious  border  is  in  effect  tacitly  acknowl- 
edged in  the  American  Ephemeris  above  referred  to,  where 
"the  adopted  semi-diameter  of  the  Sun  at  the  Earth's  mean 
distance  is  16'  02".  In  the  computations  pertaining  to 
eclipses,  Bessel's  semi-diameter  15'  59". 788  has  been 
adopted."  It  appears  to  us  that  the  explanation  in  the 
American  Ephemeris  of  the  cause  of  the  acknowledged 
spurious  diameter  of  the  Moon  is  erroneous. 

Great  Elevations  for  Observation. 

Although  our  experience  has  led  us  to  advocate  the  selec- 
tion of  great  elevations  for  astronomical  observations  of 
precision  and  research,  yet  elevation  alone  is  not  a  panacea. 
The  locality  must  present  other  favorable  orographical  con- 
ditions. Unfavorable  conditions  are  great  gulches,  canons, 
or  narrow  valleys  lying  directly  under  a  summit  and  leading 
to  it.  These  gulches  become  filled  with  highly  heated  air 
during  two  or  three  days  of  clear,  calm  weather,  and  the 
first  wind  from  below  drives  this  heated  air  over  the  summit 
and  spreads  stars  out  into  unsteady  nebulous  films;  the 
the  rings  of  Saturn  become  woolly  girdles,  the  crape  ring  is 


M.-P—  Vol.  I.]     DA  VIDSON—  APPARENT  PROJECTION,  ETC.  95 

invisible  and  the  details  of  the  belts  of  Jupiter  are  indistin- 
guishable. And  in  such  a  location  during  daytime,  obser- 
vations of  precision  on  the  Sun  are  absolutely  useless. 
The  seeing  upon  a  mountain  peak  may  be  generally  good 
when  there  is  no  snow  on  the  surface;  and  even  remarkably 
good  with  snow,  when  the  temperature  is  low  and  the  wind 
is  strong;  but  when  the  Sun  shines  and  the  temperature 
rises,  and  rapid  evaporation  takes  place  with  light  airs,  the 
seeing  becomes  very  bad.  (Experience  at  10,450  to  7,250 
feet  elevation.) 

On  Mt.  Conness,  in  the  Sierra  Nevada  (12,566  feet  ele- 
vation), the  geodetic  heliotrope  images  were  perfect  until 
the  afternoon  Sun  shone  upon  the  2,300  feet  nearly  vertical 
western  face  of  that  curious  buttress;  and  then  the  uprising, 
irregularly  warmed  atmosphere  caused  the  images  to  become 
unsteady.  During  the  quieter  moods  of  the  atmosphere, 
we  observed  Polaris  for  azimuth  in  the  middle  of  the  day 
very  satisfactorily  with  a  telescope  that  would  not  show  it 
in  daytime  at  lower  elevations  or  under  less  favorable 
conditions. 

In  1872  we  experimented  in  the  Sierra  Nevada  at  ele- 
vations from  7,200  to  9,500  feet  with  remarkable  success; 
while  another  party  of  the  United  States  Coast  and  Geo- 
detic Survey  sent  for  the  same  purpose  to  Sherman,  8,300 
feet  elevation,  in  the  Rocky  Mountains,  had  at  times  a  very 
unsteady  atmosphere.  The  Lick  Observatory  at  Mount 
Hamilton,  in  the  Diablo  Range,  at  4,209  feet  elevation,  is 
surrounded  by  unfavorable  orographical  conditions,  espe- 
cially for  observations  of  precision  in  daytime. 

It  would  appear  that  Newton  attributed  the  apparent 
unsteadiness  of  celestial  objects  to  the  disturbance  of  our 
own  atmosphere.  "  Telescopes,"  he  writes,  "cannot  be 
formed  so  as  to  take  away  that  confusion  of  rays  which 
arises  from  the  tremor  of  the  atmosphere.  The  only 
remedy  is  a  most  serene  and  quiet  air.  Such  as  may  per- 
haps be  found  on  the  tops  of  the  highest  mountains  above 
the  grosser  clouds." 

(3)  November  21,  1900. 


96  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

Precision  Observations  at   Low  Elevations. 

And  yet  there  are  climatic  conditions  at  comparatively 
low  elevations,  which  are  supremely  favorable  for  observa- 
tions of  precision  at  night.  The  experience  of  the  observ- 
ers of  the  United  States  Coast  and  Geodetic  Survey  on 
the  immense,  elevated,  arid  plains  from  El  Paso  to  San 
Diego  is  very  instructive.  During  the  hot  cloudless  days 
the  atmosphere  over  the  immediate  surface  of  the  parched 
earth  was  in  violent  unsteadiness,  and  the  heliotrope  images 
at  even  short  distances  flared  out  wildly  like  burning 
houses.  They  were  the  worst  possible  objects  for  observa- 
tions of  precision.  After  sunset  the  conditions  were  sud- 
denly changed.  With  a  cloudless  sky  and  a  minimum  of 
aqueous  vapor  in  the  attenuated  air  (Barometer  about  26 
inches)  radiation  was  quickly  effective.  The  temperature 
fell  many  degrees  in  a  short  time,  and  the  air  became 
supremely  quiet.  The  latitude  telescope  showed  stars  as 
minute  discs  with  diffraction  rings  running  along  the 
micrometer  thread  with  such  extreme  steadiness  that  it  was 
impossible  to  be  in  doubt  more  than  one-tenth  of  a  second 
of  arc  in  measurement;  and  in  the  transit  instrument  the 
star  marched  with  absolute  regularity  across  the  reticule. 
It  was  an  experience  that  an  observer  of  over  thirty  years 
in  the  field  declared  he  had  never  before  enjoyed. 

Per  contra,  on  the  low  Yolo  plains  of  the  Sacramento 
Valley  in  California,  we  have  had  the  azimuth  signal-light 
(distance  eleven  miles),  in  a  calm  night,  running  wildly  up 
and  down  the  vertical  thread  of  the  theodolite  through  five 
minutes  of  arc,  in  an  ever  changing  line  of  broken  stars  of 
the  prismatic  colors,  and  yet  showing  little  or  no  horizontal 
motion.  The  range  of  height  of  this  column  of  images  was 
eighty-seven  feet. 

In  the  great  Gangetic  plains  of  India  the  night  signals  of 
the  triangulation  parties,  when  shown  from  towers  of  fifty 
feet  elevation,  frequently  appeared  as  continuous  columns 
of  light  sixty  feet  high. 

In  the  triangulation  of  the  western  coast  of  Lower 
California   by    the  United    States    Steamer    "Thetis,"  the 


M.-P  — Vol.  I.]     DA  VIDSON- APPARENT  PROJECTION,  ETC.  97 

observer  informs  us  that  the  unsteadiness  of  the  atmosphere 
and  the  irregularity  of  the  refraction  apparently  lengthened 
the  signal  poles  to  a  hundred  feet  and  more ;  and  the  tripod 
supports  were  like  great  writhing  snakes.  Even  upon  some 
small  low  island  in  the  ocean,  where  the  climatic  conditions 
are  favorable,  the  atmosphere  at  night  becomes  very  quiet 
and  serene.  From  a  vessel's  deck  we  have  watched  the 
larger  stars  nearly  reach  the  horizon  with  very  little 
twinkling. 

Recapitulation  of  Phenomena  at  Observation. 

These  examples  are  a  few  of  the  many  experiences  in 
our  geodetic  and  astronomical  observations,  and  in  the 
descriptive  experiences  of  a  few  other  observers.  And  yet 
from  recent  publications  there  appear  to  be  many  observers 
who  do  not  understand  the  cause  of  the  phenomena,  and 
who  seem  to  think  there  must  be  something  occult  and 
unexplainable.  We  have  therefore  felt  constrained  to 
repeat  this  explanation  which  we  have  held  and  announced 
for  many  years.  It  seems  to  cover  every  phase  of  the 
phenomena. 

In  the  occultation  of  stars  by  the  Moon,  a  spurious  and 
factitious  limb  of  the  Moon  can  be  formed  only  and  solely 
by  the  unsteadiness  of  our  atmosphere  more  immediately 
surrounding  the  station  of  the  observer. 

In  a  serene  atmosphere,  the  outline  of  the  Moon  is  so 
sharp  and  clear-cut  that  the  mountains  and  valleys  thereon 
are  very  distinctively  exhibited,  and  will  bear  the  largest 
magnifying  power.  When  the  atmosphere  begins  to  change 
to  unsteadiness,  the  sharp  outline  of  the  Moon  (or  other 
object)  is  first  affected  by  tremors  or  shiverings,  which  are 
so  infrequent  that  the  observer  is  able  to  select  the  actual 
border  and  its  features.  As  the  unsteadiness  of  the  atmos- 
phere increases,  the  tremors  increase  in  frequency  and  in 
amplitude,  until  the  border  of  the  Moon  becomes  a  con- 
fused, blurred  outline,  in  which  no  serrations  can  be 
detected.  The  early  shiverings  usually  denote  the  direction 
of  movement  of  the  disturbed  air.     Under  the  atmospheric 


98  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Ser. 

conditions  of  clearness  and  serenity,  the  apparently  ap- 
proaching image  of  the  star  is  a  beautiful,  steady,  minute 
disc  with  one  or  more  delicate  diffraction  rings.  The 
Moon's  white  and  sharply  defined  border  exhibits  all  its 
serrations  and  irregularities.  As  it  approaches  the  star, 
the  diffraction  rings  disappear  in  the  increasing  light  in  the 
field  of  view,  but  the  disc  remains;  and  at  their  visible  con- 
tact the  disappearance  of  even  the  largest  and  brightest  star 
is  absolutely  instantaneous;  and  no  observer  can  be  in 
doubt  of  the  epoch  beyond  the  tenth  of  a  second.  Under 
such  favorable  atmospheric  conditions,  the  image  of  the  star 
never  enters  upon  the  visible  limb  of  the  Moon,  no  matter 
what  the  size  of  the  objective  or  the  magnifying  power 
employed.  And  with  such  conditions,  the  reappearance  of 
a  star  from  the  bright  limb  of  the  Moon  will  be  instan- 
taneous. If  the  star  were  apparently  to  make  a  near 
approach  to  the  Moon  along  the  dark  north  or  south  limb, 
where  there  are  serrations,  it  might  pass  so  close  as  to  dis- 
appear behind  the  first  mountain  and  reappear  in  the  next 
valley  (each  phenomenon  being  absolutely  instantaneous)  to 
be  swallowed  up  by  the  next  mountain,  or  in  its  absence,  to 
continue  its  visible  course.  We  have  heard  (1846)  the 
elder  Bond  describe  such  a  phenomenon  in  his  experience 
and  it  has  happened  once  to  ourselves.  But  when  the 
atmosphere  begins  to  change  to  unsteadiness,  the  star  loses 
its  diffraction  rings,  the  nucleus  is  broken  up  and  gradu- 
ally diffused  into  a  nebulous  image,  fuzzy  and  unsteady, 
with  a  brighter,  irregular,  dancing  nucleus,  or  is  spread  out 
as  a  nebulous  film  as  much  as  forty  or  fifty  seconds  of  arc 
in  diameter.  This  unsteadiness  of  the  atmosphere  throws 
the  disc  of  the  Moon  into  irregular  vibrations  or  displace- 
ments of  equal  amplitude  and  duration,  giving  it  a  factitious 
border.  With  this  disturbed  and  spurious  limb  the  Moon 
approaches  the  diffused  image  of  the  star,  both  being  in  a 
state  of  great  unsteadiness ;  but  if  the  nucleus  of  the  star 
be  sufficiently  large,  bright,  and  colored,  like  Antares  and 
Aldebaran,  the  impression  of  its  image  upon  the  retina  of 
the  eye  is  naturally  more  intense  as  an  isolated  spot  than 


M.-P.— Vol.  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.  99 

the  image  of  the  whitish,  confused,  spurious  border  of  the 
Moon,  even  when  the  former  is  within  the  latter.  The 
action  of  the  eye  is  unconsciously  selective,  but  a  certain 
effort  of  selection  is  made  under  the  less  favorable  condi- 
tion when  the  star  is  small  or  white.  There  is  no  effort  at 
selection  needed  to  receive  an  impression  of  the  Moon's 
limb,  although  the  actual  limb  may  doubtless  be  detected, 
under  high  powers,  inside  this  factitious  border.  The  im- 
pression of  the  image  of  the  star  is,  therefore,  continuous 
within  the  range  of  amplitude  of  the  excursions  of  the  disc 
of  the  Moon,  but  is  instantly  lost  when  the  limit  of  this 
range  of  vibration  is  actually  reached  by  the  apparent 
nucleus  of  the  equally  unsteady  star,  and  the  true  limb  of 
the  Moon  occults  it.  With  a  large  colored  star  all  the 
phases  of  this  phenomenon  are  unmistakable;  with  a  large 
white  star  they  may  be  somewhat  in  doubt,  as  in  the  case 
of  47  Librae  and  other  stars  elsewhere  quoted;  with  a  small 
white  star  they  will  probably  not  be  noted,  especially  in 
small  telescopes  with  low  power. 

The  exhibition  of  the  phenomenon  at  the  reappearance  of 
a  star  on  the  blurred  and  factitious  bright  limb  of  the  Moon 
should  be  in  exactly  the  reverse  order  of  the  foregoing  phe- 
nomenon of  disappearance;  and  we  have  been  fortunate  in 
looking  over  our  old  record  to  find  the  original  notes  of  the 
disappearance  of  Aldebaran  behind  the  dark  limb  of  the 
Moon,  and  its  reappearance  from  the  bright  limb,  on  March 
29,  1887,  as  elsewhere  mentioned. 

In  this  resume  we  have  confined  ourselves  to  the  exhibi- 
tion of  the  normal,  and  abnormal  conditions  in  our  atmos- 
phere attending  the  phenomenon  of  occultations  of  stars  by 
the  bright  limb  of  the  Moon,  or  by  Jupiter  or  any  other 
planet,  because  the  explanation  virtually  covers  all  associ- 
ated phenomena  in  solar  eclipses,  lunar  transits,  transits  of 
Venus  and  Mercury,  and  the  vagaries  of  star  images. 

When  our  atmosphere  is  absolutely  serene  there  is  not 
and  cannot  be  the  slightest  abnormal  exhibition  of  form, 
size,  march,  or  steadiness  of  images;  or  of  doubt  of  instanta- 
neity  in  the  epochs  observed.    Under  such  a  condition  there 


IOO  CALIFORNIA  ACADEMY  OF  SCIENCES.       [Proc.  3D  Ser. 

would  be  no  empirical  corrections  in  the  Nautical  Almanac 
to  the  semidiameters  of  the  Sun  and  Moon;  and  the  diame- 
ters of  the  planets  measured  by  different  observers,  and 
the  right  ascensions  and  delineations  of  the  stars  would  be 
consistent  within  the  instrumental  and  personal  equations. 

Other  Important  Results  Affected. 

There  is  another  and  very  important  class  of  astronomical 
results  affected  by  these  factitious  borders  of  the  Sun  and 
planets  and  the  unsteadiness  of  the  stars. 

Dr.  Newcomb  says  that  the  observed  right  ascensions  of 
the  mean  of  the  Sun's  two  limbs,  relative  to  the  fixed  stars, 
are  affected  by  personal  errors  for  which  no  means  of  elim- 
ination have  been  tried.  He  suggests  personal  error  and 
possibly  the  effect  of  the  Sun  on  the  telescope.  To  these 
causes  should  be  added  the  larger  effects  of  the  disturbed 
and  factitious  limbs;  and  in  cases  of  steadiness,  to  diffrac- 
tion of  the  limb  at  the  spider  line.  He  elsewhere  notes 
"very  large  errors,  both  accidental  and  systematic,  to  which 
observations  of  the  Sun  are  liable;"  and  again  he  regards 
"the  constant  error  in  declination  of  the  Sun  as  something 
peculiar  to  the  observer  and  the  instrument."  In  another 
place  he  says:  "There  is  a  remarkable  systematic  differ- 
ence in  the  observed  A.  R.  of  Mercury,  according  as  the 
planet  is  east  or  west  of  the  Sun,  and  therefore  according 
to  the  illuminated  side.  The  sign  of  the  result  shows  that 
the  reduction  to  the  center  of  the  planet  was  apparently  too 
small,  and  then  it  is  of  interest  to  learn  according  to  what 
law  this  error  changed  as  the  planet  moved  around  its  rela- 
tive orbit." 
^  Furthermore,  the  hurtful   effect   of   observing  upon   the 

^Jt-fJU-  or  Ls*i---t*L**-%m^  outer  Ht»b  of  the  factitious  limb  of  the  disturbed  Moon  can 

be  shown  in  the  determination  of  the  parallactic  inequality 
of  the  Moon  from  meridian  observations.  Dr.  Newcomb 
says  the  method  is  peculiarly  liable  to  systematic  error, 
owing  to  the  fact  that  observations  have  to  be  made  on  one 
limb  of  the  Moon  when  the  inequality  is  positive,  and  on 
the  other  limb  when  it  is  negative.     Hence  if  we  determine 


M.-P— Vol.  I.]     DAVIDSON— APPARENT  PROJECTION,  ETC.        IOI 

the  inequality  (125". 5)  by  the  comparison  of  its  extreme 
observed  effects  on  the  Moon's  right  ascension,  any  error  in 
the  adopted  semidiameter  will  affect  the  result  by  its  full 
amount.  This  suggests  that  this  gravitational  method  of 
determining  the  Solar  Parallax  would  be  more  accurately 
employed  by  observing  occultations  of  stars  large  enough 
to  be  seen  through  the  spurious  bright  limb  of  the  Moon. 
Moreover,  the  observations  themselves  would  afford  some 
data  for  the  elimination  of  the  error  depending  upon  a  fac- 
titious limb. 

Nearly  all  Measured  Diameters  Too  Large. 

In  all  instrumental  observations  for  the  right  ascension  of 
the  Sun  or  Moon,  and  for  their  declination  and  diameter, 
it  must  be  evident  that  the  observer  obtains  accurate  meas- 
ures only  when  the  disc  of  either  body  is  sharply  defined, 
devoid  of  tremor  or  unsteadiness,  and  unaffected  by  irregu- 
lar and  extraordinary  refraction,  without  reckoning  diffrac- 
tion at  the  spider  line,  unknown  instrumental  errors,  and 
peculiarities  of  observation.  As  these  supreme  conditions 
of  steadiness  are  seldom  obtained,  it  necessarily  follows  that 
the  mean  of  any  number  of  observations  taken  under  differ- 
ent atmospheric  conditions  (say  for  example  the  diameter 
of  the  Sun,  Moon,  or  planets)  must  be  too  large.  The 
diameter  can  only  be  too  small  through  error  of  observation, 
instrumental  errors,  diffraction  of  the  spider  line,  or  abnor- 
mal refraction. 

With  a  disturbed  atmosphere  in  observations  for  the  deter- 
mination of  the  right  ascension  of  the  Moon  during  the  first 
half  of  a  lunation,  the  observed  A.  R.  of  the  limb  will  be 
too  small  and  for  the  second  half  too  large.  Similar  results 
will  follow  from  observations  of  the  I  and  II  limbs  of  the 
Sun  and  planets.  Therefore  all  published  diameters  of  the 
Sun,  Moon  and  planets  derived  directly  from  actual  obser- 
vations must  be  too  large.  Moreover,  this  presents  a  case 
where  the  mean  of  measured  quantities  is  not  the  most 
probable  value.  The  mean  of  all  the  minimum  measures 
would  be  nearer  the  truth. 


102  CALIFORNIA  ACADEMY  OF  SCIENCES.        [Proc.  3D  Sbr. 

The  amplitude  of  the  excursions  of  the  images  of  the 
Sun,  Moon,  and  planets  in  a  disturbed  atmosphere  is  a  vari- 
able quantity  that  can  not  be  determined  but  should  be 
avoided  if  practicable.  To  obtain  the  most  trustworthy 
results  in  reasonable  time,  we  need  the  fixed  observatories 
located  at  points  which  conspire  to  give  the  best  atmospheric 
conditions  determined  upon  after  systematic  and  exhaustive 
trial  for  special  lines  of  research ;  the  highest  class  of  instru- 
mentation; observers  with  ideal  eyes  (of  which  unfortu- 
nately there  are  very  few)  ;  discrimination  in  the  selection 
of  proper  times  of  observation;  and  a  wise  rejection  of 
observations  made  under  abnormal  conditions. 

Note.  Since  this  paper  was  presented  to  the  California  Academy  of 
Sciences,  Professor  A.  E.  Douglass  of  the  Lowell  Observatory  at  Flagstaff, 
Arizona,  has  published  the  second  of  his  interesting  papers  upon  "The 
Atmosphere,  Telescope  and  Observer,"  and  "Scales  of  Seeing."  Pop. 
Astr.  1898. 


MATHEMATICAL-PHYSICAL. 
Vol.  I. 

No.  i— On  Rational  Quadratic  Transformations.  By  M.  W.  ^j 
Haskell j 

No.   2— The  Quadratic  Cremona  Transformation.     By  Leonard  E.   f     $.35 
Dickson ! 

No.   3 — On  Curvilinear  Asymptotes.     By  M.  W.  Haskell J 

No.   4— Systems  of  Simple    Groups  derived    from    the  Orthogonal 

Group.     By  Leonard  E.  Dickson .25 

No.  5 — Systems  of  Simple  Groups  derived  from  the  Orthogonal  "^ 
Group.     (Second  Paper.)     By  Leonard  E.  Dickson ! 

No.  6 — On  an  m  n2  Parameter  Group  of  Linear  Substitutions  in  { 
m  n  Variables.     By  E.  J.  Wilczynski J 

No.  7 — The  Apparent  Projection  of  Stars  upon  the  Bright  Limb^J 
of  the  Moon  at  Occultation,  and  Similar  Phenomena  at  ( 
Total  Solar  Eclipses,  Transits  of  Venus  and  Mercury,  { 
Etc.,  Etc.     By  George  Davidson,  Ph.D.,  Sc.D J 


All  subscriptions,  applications  for  exchanges,  and  inquiries  concerning  the 
publications  should  be  addressed  to 

J.  O'B.  GUNN,  Corresponding  Secretary, 

California  Academy  of  Sciences, 

San  Francisco,  California. 


